A064840 a(n) = tau(n)*sigma(n).
1, 6, 8, 21, 12, 48, 16, 60, 39, 72, 24, 168, 28, 96, 96, 155, 36, 234, 40, 252, 128, 144, 48, 480, 93, 168, 160, 336, 60, 576, 64, 378, 192, 216, 192, 819, 76, 240, 224, 720, 84, 768, 88, 504, 468, 288, 96, 1240, 171, 558, 288, 588, 108, 960, 288, 960, 320, 360
Offset: 1
Examples
For n = 10, a(10) = sigma(10) * tau(10) = 18 * 4 = 72. - _Indranil Ghosh_, Jan 20 2017
Links
- Indranil Ghosh, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)
- Vaclav Kotesovec, Graph - the asymptotic ratio
Programs
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Magma
[ NumberOfDivisors(n)*SumOfDivisors(n) : n in [1..40]];
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Maple
with(numtheory): seq(sigma(n)*tau(n), n=1..58) ; # Zerinvary Lajos, Jun 04 2008
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Mathematica
Table[ DivisorSigma[0, n] * DivisorSigma[1, n], {n, 1, 58}] (* Jean-François Alcover, Mar 26 2013 *) -
PARI
{ for (n=1, 1000, a=numdiv(n)*sigma(n); write("b064840.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 28 2009
Formula
Multiplicative with a(p^e) = (p^(e+1)-1)*(e+1)/(p-1). a(n) = (1/2)*Sum_{i|n, j|n} (i+j).
Dirichlet g.f. (zeta(s)*zeta(s-1))^2/zeta(2s-1). - R. J. Mathar, Feb 11 2011
Sum_{k=1..n} a(k) ~ Pi^4 * n^2 / (144*Zeta(3)) * (2*log(n) - 1 + 4*gamma - 4*Zeta'(3)/Zeta(3) + 24*Zeta'(2)/Pi^2), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jan 31 2019
Comments