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 A059378 Jordan function J_5(n). 17
 1, 31, 242, 992, 3124, 7502, 16806, 31744, 58806, 96844, 161050, 240064, 371292, 520986, 756008, 1015808, 1419856, 1822986, 2476098, 3099008, 4067052, 4992550, 6436342, 7682048, 9762500, 11510052, 14289858, 16671552, 20511148 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 199, #3. R. Sivaramakrishnan, "The many facets of Euler's totient. II. Generalizations and analogues", Nieuw Arch. Wisk. (4) 8 (1990), no. 2, 169-187. LINKS T. D. Noe, Table of n, a(n) for n=1..1000 FORMULA a(n) = sum(d|n, d^5*mu(n/d)). - Benoit Cloitre, Apr 05 2002 Multiplicative with a(p^e) = p^(5e)-p^(5(e-1)). Dirichlet generating function: zeta(s-5)/zeta(s). - Franklin T. Adams-Watters, Sep 11 2005. a(n) = n^5*Product_{distinct primes p dividing n} (1-1/p^5). - Tom Edgar, Jan 09 2015 G.f.: Sum_{n>=1} a(n)*x^n/(1 - x^n) = x*(1 + 26*x + 66*x^2 + 26*x^3 + x^4)/(1 - x)^6. - Ilya Gutkovskiy, Apr 25 2017 Sum_{k=1..n} a(k) ~ 315*n^6 / (2*Pi^6). - Vaclav Kotesovec, Feb 07 2019 MAPLE J := proc(n, k) local i, p, t1, t2; t1 := n^k; for p from 1 to n do if isprime(p) and n mod p = 0 then t1 := t1*(1-p^(-k)); fi; od; t1; end; # (with k = 5) MATHEMATICA JordanJ[n_, k_] := DivisorSum[n, #^k*MoebiusMu[n/#] &]; f[n_] := JordanJ[n, 5]; Array[f, 30] PROG (PARI) for(n=1, 100, print1(sumdiv(n, d, d^5*moebius(n/d)), ", ")) (PARI) { for (n = 1, 1000, write("b059378.txt", n, " ", sumdiv(n, d, d^5*moebius(n/d))); ) } \\ Harry J. Smith, Jun 26 2009 (Python) from sympy import divisors, mobius def a(n): return sum([d**5*mobius(n/d) for d in divisors(n)]) # Indranil Ghosh, Apr 26 2017 CROSSREFS See A059379 and A059380 (triangle of values of J_k(n)), A000010 (J_1), A059376 (J_3), A059377 (J_4). Sequence in context: A173832 A272162 A189923 * A024003 A258807 A221848 Adjacent sequences:  A059375 A059376 A059377 * A059379 A059380 A059381 KEYWORD nonn,mult AUTHOR N. J. A. Sloane, Jan 28 2001 STATUS approved

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Last modified October 14 14:20 EDT 2019. Contains 328017 sequences. (Running on oeis4.)