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A069094 Jordan function J_9(n). 3
1, 511, 19682, 261632, 1953124, 10057502, 40353606, 133955584, 387400806, 998046364, 2357947690, 5149441024, 10604499372, 20620692666, 38441386568, 68585259008, 118587876496, 197961811866, 322687697778, 510999738368 (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..5000

Wikipedia, Jordan's totient function

FORMULA

a(n) = Sum_{d|n} d^9*mu(n/d).

Multiplicative with a(p^e) = p^(9e)-p^(9(e-1)).

Dirichlet generating function: zeta(s-9)/zeta(s). - Ralf Stephan, Jul 04 2013

a(n) = n^9*Product_{distinct primes p dividing n} (1-1/p^9). - Tom Edgar, Jan 09 2015

Sum_{k=1..n} a(k) ~ 18711*n^10 / (2*Pi^10). - Vaclav Kotesovec, Feb 07 2019

MATHEMATICA

JordanJ[n_, k_] := DivisorSum[n, #^k*MoebiusMu[n/#] &]; f[n_] := JordanJ[n, 9]; Array[f, 22]

PROG

(PARI) for(n=1, 100, print1(sumdiv(n, d, d^9*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: A228265 A228224 A022525 * A024007 A258810 A321554

Adjacent sequences:  A069091 A069092 A069093 * A069095 A069096 A069097

KEYWORD

easy,nonn,mult

AUTHOR

Benoit Cloitre, Apr 05 2002

STATUS

approved

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Last modified January 25 01:49 EST 2020. Contains 331229 sequences. (Running on oeis4.)