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A059378 Jordan function J_5(n). 21
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

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

CROSSREFS

See A059379 and A059380 (triangle of values of J_k(n)), A000010 (J_1), A059376 (J_3), A059377 (J_4), A059378 (J_5).

Sequence in context: A082544 A173832 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 August 27 17:19 EDT 2015. Contains 261095 sequences.