Revision History for A357879
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing all changes.
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#7 by Michael De Vlieger at Thu Oct 27 10:13:30 EDT 2022
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#6 by Gus Wiseman at Thu Oct 27 09:59:30 EDT 2022
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#5 by Gus Wiseman at Thu Oct 27 09:58:36 EDT 2022
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| EXAMPLE
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The a(3600) = 5 divisors, their prime indices, and theirthe prime indices of their quotients:
45: {2,2,3} * {1,1,1,1,3}
50: {1,3,3} * {1,1,1,2,2}
60: {1,1,2,3} * {1,1,2,3}
72: {1,1,1,2,2} * {1,3,3}
80: {1,1,1,1,3} * {2,2,3}
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#4 by Gus Wiseman at Thu Oct 27 09:28:02 EDT 2022
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| CROSSREFS
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Cf. A033879, A033880, A064914, A181819, A213074, A235130, A237258, A276107, A300061, A321144, A357975.
Cf. A118914, A181819, `A300273, `A304442.
Cf. A064914, A213074, A213086, A235130, A237194, A237258, A276107, `A300061.
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#3 by Gus Wiseman at Thu Oct 27 09:22:51 EDT 2022
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| NAME
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Number of divisors of n with the same sum of prime indices as their quotient. Central column of A321144, taking gaps as 0's.
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| CROSSREFS
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Cf. A033879 2minus_sumdiv, A033880 sumdiv_minus2, A321144 tri_numdiv_sumprix_k, A357975 half_prix_floor.
Cf. A047966 ptns_unif, A118914 pri_sig_sort, A181819 pri_shadow, A300273 h_collapsible, A304442 ptns_w_eq_runsums.
Cf. A033879, A033880, A321144, A357975.
Cf. A118914, A181819, `A300273, `A304442.
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#2 by Gus Wiseman at Thu Oct 27 09:18:08 EDT 2022
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| NAME
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allocatedNumber of divisors of n with the same sum of prime indices as their quotient. Central forcolumn Gusof WisemanA321144.
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| DATA
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1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0
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| OFFSET
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1,12
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| COMMENTS
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A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
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| EXAMPLE
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The a(3600) = 5 divisors and their prime indices:
45: {2,2,3}
50: {1,3,3}
60: {1,1,2,3}
72: {1,1,1,2,2}
80: {1,1,1,1,3}
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| MATHEMATICA
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sumprix[n_]:=Total[Cases[FactorInteger[n], {p_, k_}:>k*PrimePi[p]]];
Table[Length[Select[Divisors[n], sumprix[#]==sumprix[n]/2&]], {n, 100}]
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| CROSSREFS
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Positions of nonzero terms are A357976, counted by A002219.
A001222 counts prime factors, distinct A001221.
A056239 adds up prime indices, row sums of A112798.
Cf. A033879 2minus_sumdiv, A033880 sumdiv_minus2, A321144 tri_numdiv_sumprix_k, A357975 half_prix_floor.
Cf. A047966 ptns_unif, A118914 pri_sig_sort, A181819 pri_shadow, A300273 h_collapsible, A304442 ptns_w_eq_runsums.
Cf. A064914, A213074, A213086, A235130, A237194, A237258, A276107, `A300061.
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| KEYWORD
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allocated
nonn
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| AUTHOR
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Gus Wiseman, Oct 27 2022
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| STATUS
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approved
editing
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#1 by Gus Wiseman at Mon Oct 17 17:50:43 EDT 2022
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| NAME
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allocated for Gus Wiseman
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| KEYWORD
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allocated
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| STATUS
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approved
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