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 A053820 a(n) = Sum_{k=1..n, gcd(n,k) = 1} k^4. 6
 1, 1, 17, 82, 354, 626, 2275, 3108, 7395, 9044, 25333, 17668, 60710, 50470, 88388, 103496, 243848, 129750, 432345, 266088, 497574, 497178, 1151403, 539912, 1541770, 1153724, 1900089, 1516844, 3756718, 1246568, 5273999 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS If gcd(n,30) = 1, then a(n) is divisible by n. If n has at least one prime factor == 1 (mod 30), then a(n) is divisible by n. - Jianing Song, Jul 13 2018 REFERENCES T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 48, problem 15, the function phi_4(n). L. E. Dickson, History of the Theory of Numbers, Vol. I (Reprint 1966), p. 140. LINKS Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi) John D. Baum, A Number-Theoretic Sum, Mathematics Magazine 55.2 (1982): 111-113. P. G. Brown, Some comments on inverse arithmetic functions, Math. Gaz. 89 (2005) 403-408. FORMULA a(n) = (6*n^4*A000010(n)+10*n^3*A023900(n)-n*A063453(n))/30 for n>1. Formula is derived from a more general formula of A. Thacker (1850), see [Dickson, Brown]. - Franz Vrabec, Aug 21 2005 G.f. A(x) satisfies: A(x) = x*(1 + 11*x + 11*x^2 + x^3)/(1 - x)^6 - Sum_{k>=2} k^4 * A(x^k). - Ilya Gutkovskiy, Mar 29 2020 MATHEMATICA a[n_] := Sum[If[GCD[n, k] == 1, k^4, 0], {k, 1, n}]; Table[a[n], {n, 1, 31}] (* Jean-François Alcover, Feb 26 2014 *) PROG (PARI) a(n) = sum(k=1, n, (gcd(n, k) == 1)*k^4); \\ Michel Marcus, Feb 26 2014 CROSSREFS Column k=4 of A308477. Sequence in context: A065960 A017671 A001159 * A294288 A296401 A259142 Adjacent sequences:  A053817 A053818 A053819 * A053821 A053822 A053823 KEYWORD nonn AUTHOR N. J. A. Sloane, Apr 07 2000 STATUS approved

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Last modified August 15 08:53 EDT 2020. Contains 336487 sequences. (Running on oeis4.)