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 A013954 a(n) = sigma_6(n), the sum of the 6th powers of the divisors of n. 92
 1, 65, 730, 4161, 15626, 47450, 117650, 266305, 532171, 1015690, 1771562, 3037530, 4826810, 7647250, 11406980, 17043521, 24137570, 34591115, 47045882, 65019786, 85884500, 115151530, 148035890 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If the canonical factorization of n into prime powers is the product of p^e(p) then sigma_k(n) = Product_p ((p^((e(p)+1)*k))-1)/(p^k-1). Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001 Inverse Mobius transform of A001014. - R. J. Mathar, Oct 13 2011 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 FORMULA G.f.: sum_{k>=1} k^6*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003 L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^5)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 06 2017 MAPLE A013954 := proc(n)         numtheory[sigma][6](n) ; end proc: # R. J. Mathar, Oct 13 2011 MATHEMATICA lst={}; Do[AppendTo[lst, DivisorSigma[6, n]], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *) PROG (Sage) [sigma(n, 6)for n in range(1, 24)] # Zerinvary Lajos, Jun 04 2009 (PARI) a(n)=sigma(n, 6) \\ Charles R Greathouse IV, Apr 28, 2011 (MAGMA) [DivisorSigma(6, n): n in [1..30]]; // Bruno Berselli, Apr 10 2013 CROSSREFS Sequence in context: A321562 A034680 A017675 * A294301 A116277 A220389 Adjacent sequences:  A013951 A013952 A013953 * A013955 A013956 A013957 KEYWORD nonn,mult,easy AUTHOR STATUS approved

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Last modified January 24 10:41 EST 2021. Contains 340399 sequences. (Running on oeis4.)