|
| |
|
|
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
Sum_{k=1..n} a(k) ~ n^9 / (9*Zeta(9)). - Vaclav Kotesovec, Feb 07 2019
|
|
|
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
|
| |
|
|
