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 A344060 a(n) = Sum_{d|n} sigma(d)^n. 3
 1, 10, 65, 2483, 7777, 2990810, 2097153, 2568661988, 10604761518, 3570527751850, 743008370689, 232227195048256531, 793714773254145, 21035724521219881850, 504857283427304833025, 727429690188773950335429, 2185911559738696531969, 43567528891100073055151954340, 5242880000000000000000001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..19. FORMULA G.f.: Sum_{k >= 1} (sigma(k) * x)^k/(1 - (sigma(k) * x)^k). If p is prime, a(p) = 1 + (p+1)^p. MATHEMATICA a[n_] := DivisorSum[n, DivisorSigma[1 , #]^n &]; Array[a, 19] (* Amiram Eldar, May 08 2021 *) PROG (PARI) a(n) = sumdiv(n, d, sigma(d)^n); (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (sigma(k)*x)^k/(1-(sigma(k)*x)^k))) CROSSREFS Cf. A007429, A023887, A065018, A342471, A344044, A344047, A344061. Sequence in context: A262342 A307144 A344047 * A140362 A159838 A269679 Adjacent sequences: A344057 A344058 A344059 * A344061 A344062 A344063 KEYWORD nonn AUTHOR Seiichi Manyama, May 08 2021 STATUS approved

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Last modified September 9 10:46 EDT 2024. Contains 375764 sequences. (Running on oeis4.)