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A069095 Jordan function J_10(n). 4
1, 1023, 59048, 1047552, 9765624, 60406104, 282475248, 1072693248, 3486725352, 9990233352, 25937424600, 61855850496, 137858491848, 288972178704, 576640565952, 1098437885952, 2015993900448, 3566920035096, 6131066257800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

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

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = sum(d|n, d^10*mu(n/d)).

Multiplicative with a(p^e) = p^(10e)-p^(10(e-1)).

Dirichlet generating function: zeta(s-10)/zeta(s). - Ralf Stephan, Jul 04 2013

a(n) = n^10*Product_{distinct primes p dividing n} (1-1/p^10). - Tom Edgar, Jan 09 2015

MAPLE

f:= n -> n^10*mul(1-1/p^10, p=numtheory:-factorset(n)):

map(f, [$1..30]); # Robert Israel, Jan 09 2015

MATHEMATICA

JordanJ[n_, k_] := DivisorSum[n, #^k*MoebiusMu[n/#] &]; f[n_] := JordanJ[n, 10]; Array[f, 21]

PROG

(PARI) for(n=1, 100, print1(sumdiv(n, d, d^10*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: A075947 A228266 A022526 * A024008 A123867 A160959

Adjacent sequences:  A069092 A069093 A069094 * A069096 A069097 A069098

KEYWORD

easy,nonn,mult

AUTHOR

Benoit Cloitre, Apr 05 2002

STATUS

approved

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Last modified December 9 06:30 EST 2016. Contains 278963 sequences.