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A303759

Number of times the largest prime power factor of n (A034699) is largest prime power factor for numbers <= n; a(1) = 1.

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 2, 1, 4, 3, 2, 1, 2, 1, 2, 1, 4, 1, 5, 1, 1, 3, 2, 5, 3, 1, 2, 3, 3, 1, 6, 1, 4, 4, 2, 1, 2, 1, 2, 3, 4, 1, 2, 5, 4, 3, 2, 1, 6, 1, 2, 5, 1, 5, 6, 1, 4, 3, 7, 1, 6, 1, 2, 3, 4, 7, 6, 1, 3, 1, 2, 1, 8, 5, 2, 3, 8, 1, 7, 7, 4, 3, 2, 5, 2, 1, 2, 9, 4, 1, 6, 1, 8, 9

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OFFSET

1,6

COMMENTS

Ordinal transform of A034699.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

MAPLE

b:= proc() 0 end:

a:= proc(n) option remember; local t;

t:= max(1, seq(i[1]^i[2], i=ifactors(n)[2]));

b(t):= b(t)+1

end:

seq(a(n), n=1..120); # Alois P. Heinz, Apr 30 2018

MATHEMATICA

f[n_] := Max[Power @@@ FactorInteger[n]];

b[_] = 0;

a[n_] := With[{t = f[n]}, b[t] = b[t]+1];

Array[a, 105] (* Jean-François Alcover, Jan 03 2022 *)

PROG

(PARI)

up_to = 65537;

ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om, invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om, invec[i], (1+pt))); outvec; };

A034699(n) = if(1==n, n, fordiv(n, d, if(isprimepower(n/d), return(n/d))));

v303759 = ordinal_transform(vector(up_to, n, A034699(n)));

A303759(n) = v303759[n];

CROSSREFS

Cf. A000961 (positions of ones), A034699.

Cf. also A078899, A284600, A302789.

Sequence in context: A356553 A324369 A276781 * A330754 A330753 A082068

Adjacent sequences: A303756 A303757 A303758 * A303760 A303761 A303762

KEYWORD

nonn

AUTHOR

Antti Karttunen, Apr 30 2018

STATUS

approved