Revision History for A123707
(Underlined text is an addition;
strikethrough text is a deletion.)
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#9 by Susanna Cuyler at Thu Feb 06 14:50:14 EST 2020
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#8 by Ilya Gutkovskiy at Thu Feb 06 14:12:17 EST 2020
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#7 by Ilya Gutkovskiy at Thu Feb 06 13:27:19 EST 2020
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| FORMULA
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G.f.: Sum_{k>=1} mu(k) * x^k * (1 - x^k) / (1 - 2*x^k). - Ilya Gutkovskiy, Feb 06 2020
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| MATHEMATICA
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t[n_, k_] := If[Divisible[n, k], MoebiusMu[n/k], 0] - If[Divisible[n, k + 1], MoebiusMu[n/(k + 1)], 0]; Table[Sum[t[n, k]*2^(k - 1), {k, 1, n}], {n, 1, 50}] (* _G. C. GreublGreubel_, Oct 26 2017 *)
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| STATUS
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approved
editing
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#6 by Paul D. Hanna at Thu Oct 26 23:01:38 EDT 2017
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#5 by G. C. Greubel at Thu Oct 26 21:28:36 EDT 2017
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Discussion
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| Thu Oct 26
| 23:01
| Paul D. Hanna: Thank you for the update!
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#4 by G. C. Greubel at Thu Oct 26 21:28:29 EDT 2017
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| LINKS
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G. C. Greubel, <a href="/A123707/b123707.txt">Table of n, a(n) for n = 1..1000</a>
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| MATHEMATICA
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t[n_, k_] := If[Divisible[n, k], MoebiusMu[n/k], 0] - If[Divisible[n, k + 1], MoebiusMu[n/(k + 1)], 0]; Table[Sum[t[n, k]*2^(k - 1), {k, 1, n}], {n, 1, 50}] (* _G. C. Greubl_, Oct 26 2017 *)
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approved
editing
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#3 by Russ Cox at Fri Mar 30 18:37:01 EDT 2012
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| AUTHOR
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_Paul D. Hanna (pauldhanna(AT)juno.com), _, Oct 09 2006
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Discussion
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| Fri Mar 30
| 18:37
| OEIS Server: https://oeis.org/edit/global/213
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#2 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007
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| KEYWORD
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nonn,new
nonn
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| AUTHOR
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Paul D . Hanna (pauldhanna(AT)juno.com), Oct 09 2006
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#1 by N. J. A. Sloane at Wed Dec 06 03:00:00 EST 2006
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| NAME
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a(n) = Sum_{k=1..n} A123706(n,k)*2^(k-1).
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| DATA
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1, 0, 1, 3, 7, 14, 31, 60, 126, 248, 511, 1005, 2047, 4064, 8183, 16320, 32767, 65394, 131071, 261885, 524255, 1048064, 2097151, 4193220, 8388600, 16775168, 33554304, 67104765, 134217727, 268427002, 536870911, 1073725440, 2147483135
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| OFFSET
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1,4
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| COMMENTS
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Triangle A123706 is the matrix inverse of triangle A010766(n,k) = [n/k].
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| PROG
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(PARI) {a(n)=sum(k=1, n, (matrix(n, n, r, c, if(r>=c, floor(r/c)))^-1)[n, k]*2^(k-1))}
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| CROSSREFS
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Cf. A123706, A123708, A123709.
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| KEYWORD
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nonn
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| AUTHOR
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Paul D Hanna (pauldhanna(AT)juno.com), Oct 09 2006
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| STATUS
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approved
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