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Search: id:A038040
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| A038040 |
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d(n)*n, where d(n) = number of divisors of n. |
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+0
16
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| 1, 4, 6, 12, 10, 24, 14, 32, 27, 40, 22, 72, 26, 56, 60, 80, 34, 108, 38, 120, 84, 88, 46, 192, 75, 104, 108, 168, 58, 240, 62, 192, 132, 136, 140, 324, 74, 152, 156, 320, 82, 336, 86, 264, 270, 184, 94, 480, 147, 300, 204, 312, 106, 432, 220, 448, 228, 232, 118
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Dirichlet convolution of sigma(n) with phi(n) - Michael Somos, Jun 08, 2000
a(n) = n*log(n) + (2G-1)n + O(sqrt(n)), G=eulergamma (Dirichlet).
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LINKS
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P. Pollack, Analytic and Combinatorial Number Theory Course Notes, p. 147.
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FORMULA
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Dirichlet g.f.: zeta(s-1)^2.
G.f.: Sum_{n>=1} n*x^n/(1-x^n)^2. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Dec 30 2001
Sum_{k=1..n} sigma(gcd(n, k)). Multiplicative with a(p^e) = (e+1)*p^e. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Oct 30 2001
Equals A127648 * A127093 * the harmonic series, [1/1, 1/2, 1/3,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 10 2007
Equals row sums of triangle A127528 - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 21 2007
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MAPLE
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with(numtheory): A038040 := n->sigma[0](n)*n;
with(numtheory):seq(n*tau(n), n=1..59) ; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 04 2008
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PROGRAM
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(PARI) a(n)=if(n<1, 0, direuler(p=2, n, 1/(1-p*X)^2)[n])
(PARI) a(n)=if(n<1, 0, polcoeff(sum(k=1, n, k*x^k/(x^k-1)^2, x*O(x^n)), n)) /* Michael Somos Jan 29 2005 */
(MuPad)n*numlib::tau (n)$ n=1..90 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 13 2008
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CROSSREFS
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Cf. A000005, A000010, A000203, A029935, A064987, A062952.
Cf. A127648, A127093, A127528.
Sequence in context: A114413 A110758 A074162 this_sequence A058270 A058199 A110178
Adjacent sequences: A038037 A038038 A038039 this_sequence A038041 A038042 A038043
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KEYWORD
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nonn,easy,mult
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net)
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