|
Search: id:A059378
|
|
|
| A059378 |
|
Jordan function J_5(n). |
|
+0
13
|
|
| 1, 31, 242, 992, 3124, 7502, 16806, 31744, 58806, 96844, 161050, 240064, 371292, 520986, 756008, 1015808, 1419856, 1822986, 2476098, 3099008, 4067052, 4992550, 6436342, 7682048, 9762500, 11510052, 14289858, 16671552, 20511148
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
REFERENCES
|
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 199, #3.
R. Sivaramakrishnan, "The many facets of Euler's totient. II. Generalizations and analogues", Nieuw Arch. Wisk. (4) 8 (1990), no. 2, 169-187.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=1..1000
|
|
FORMULA
|
a(n)=sum(d|n, d^5*mu(n/d)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 05 2002
Multiplicative with a(p^e) = p^(5e)-p^(5(e-1)).
Dirichlet generating function: zeta(s-5)/zeta(s). - Franklin T. Adams-Watters, Sep 11 2005.
|
|
MAPLE
|
J := proc(n, k) local i, p, t1, t2; t1 := n^k; for p from 1 to n do if isprime(p) and n mod p = 0 then t1 := t1*(1-p^(-k)); fi; od; t1; end; # (with k = 5)
|
|
PROGRAM
|
(PARI) for(n=1, 100, print1(sumdiv(n, d, d^5*moebius(n/d)), ", "))
(PARI) { for (n = 1, 1000, write("b059378.txt", n, " ", sumdiv(n, d, d^5*moebius(n/d))); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 26 2009]
|
|
CROSSREFS
|
See 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: A059899 A140846 A082544 this_sequence A024003 A147963 A027846
Adjacent sequences: A059375 A059376 A059377 this_sequence A059379 A059380 A059381
|
|
KEYWORD
|
nonn,mult
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Jan 28 2001
|
|
|
Search completed in 0.002 seconds
|
