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Search: id:A059378
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| A059378 |
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Jordan function J_5(n). |
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+0
13
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| 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)
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OFFSET
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1,2
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REFERENCES
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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.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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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.
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MAPLE
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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)
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PROGRAM
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(PARI) for(n=1, 100, print1(sumdiv(n, d, d^5*moebius(n/d)), ", "))
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CROSSREFS
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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 A027846 A042872
Adjacent sequences: A059375 A059376 A059377 this_sequence A059379 A059380 A059381
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KEYWORD
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nonn,mult
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AUTHOR
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njas, Jan 28 2001
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