Search: id:A059378
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%I A059378
%S A059378 1,31,242,992,3124,7502,16806,31744,58806,96844,161050,240064,371292,
%T A059378 520986,756008,1015808,1419856,1822986,2476098,3099008,4067052,
%U A059378 4992550,6436342,7682048,9762500,11510052,14289858,16671552,20511148
%N A059378 Jordan function J_5(n).
%D A059378 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 199, #3.
%D A059378 R. Sivaramakrishnan, "The many facets of Euler's totient. II. Generalizations 
               and analogues", Nieuw Arch. Wisk. (4) 8 (1990), no. 2, 169-187.
%H A059378 T. D. Noe, <a href="b059378.txt">Table of n, a(n) for n=1..1000</a>
%F A059378 a(n)=sum(d|n, d^5*mu(n/d)) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Apr 05 2002
%F A059378 Multiplicative with a(p^e) = p^(5e)-p^(5(e-1)).
%F A059378 Dirichlet generating function: zeta(s-5)/zeta(s). - Franklin T. Adams-Watters, 
               Sep 11 2005.
%p A059378 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)
%o A059378 (PARI) for(n=1,100,print1(sumdiv(n,d,d^5*moebius(n/d)),","))
%o A059378 (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]
%Y A059378 See A059379 and A059380 (triangle of values of J_k(n)), A000010 (J_1), 
               A059376 (J_3), A059377 (J_4), A059378 (J_5).
%Y A059378 Sequence in context: A059899 A140846 A082544 this_sequence A024003 A147963 
               A027846
%Y A059378 Adjacent sequences: A059375 A059376 A059377 this_sequence A059379 A059380 
               A059381
%K A059378 nonn,mult
%O A059378 1,2
%A A059378 N. J. A. Sloane (njas(AT)research.att.com), Jan 28 2001

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