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A069092 Jordan function J_7(n). 2
1, 127, 2186, 16256, 78124, 277622, 823542, 2080768, 4780782, 9921748, 19487170, 35535616, 62748516, 104589834, 170779064, 266338304, 410338672, 607159314, 893871738, 1269983744, 1800262812, 2474870590, 3404825446, 4548558848 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

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

LINKS

E. Pérez Herrero, Table of n, a(n) for n=1..2000

FORMULA

a(n) = sum(d|n, d^7*mu(n/d)).

Multiplicative with a(p^e) = p^(7e)-p^(7(e-1)).

Dirichlet generating function: zeta(s-7)/zeta(s). - Ralf Stephan, Jul 04 2013

a(n) = n^7*Product_{distinct primes p dividing n} (1-1/p^7). - Tom Edgar, Jan 09 2015

Sum_{k=1..n} a(k) ~ 4725*n^8 / (4*Pi^8). - Vaclav Kotesovec, Feb 07 2019

MATHEMATICA

JordanTotient[n_, k_: 1] := DivisorSum[n, (#^k)*MoebiusMu[n/# ] &] /; (n > 0) && IntegerQ[n]

A069092[n_] := JordanTotient[n, 7]; (* Enrique Pérez Herrero, Nov 02 2010 *)

PROG

(PARI) for(n=1, 100, print1(sumdiv(n, d, d^7*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).

Cf. A069091 (J_6), A069092 (J_7), A069093 (J_8), A069094 (J_9), A069095 (J_10). [Enrique Pérez Herrero, Nov 02 2010]

Sequence in context: A022523 A090029 A152726 * A024005 A258808 A321552

Adjacent sequences:  A069089 A069090 A069091 * A069093 A069094 A069095

KEYWORD

easy,nonn,mult

AUTHOR

Benoit Cloitre, Apr 05 2002

STATUS

approved

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Last modified September 15 04:09 EDT 2019. Contains 327062 sequences. (Running on oeis4.)