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A069093 Jordan function J_8(n). 5
1, 255, 6560, 65280, 390624, 1672800, 5764800, 16711680, 43040160, 99609120, 214358880, 428236800, 815730720, 1470024000, 2562493440, 4278190080, 6975757440, 10975240800, 16983563040, 25499934720, 37817088000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 199, #3.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = Sum_{d|n} d^8*mu(n/d).

Multiplicative with a(p^e) = p^(8e)-p^(8(e-1)).

Dirichlet generating function: zeta(s-8)/zeta(s). - Ralf Stephan, Jul 04 2013

a(n) = n^8*Product_{distinct primes p dividing n} (1-1/p^8). - Tom Edgar, Jan 09 2015

MATHEMATICA

JordanJ[n_, k_] := DivisorSum[n, #^k*MoebiusMu[n/#] &]; f[n_] := JordanJ[n, 8]; Array[f, 25]

PROG

(PARI) for(n=1, 100, print1(sumdiv(n, d, d^8*moebius(n/d)), ", "))

CROSSREFS

Cf. 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: A228223 A022524 A261032 * A024006 A258809 A321553

Adjacent sequences:  A069090 A069091 A069092 * A069094 A069095 A069096

KEYWORD

easy,nonn,mult

AUTHOR

Benoit Cloitre, Apr 05 2002

STATUS

approved

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Last modified December 12 07:07 EST 2018. Contains 318053 sequences. (Running on oeis4.)