Search: id:A059376
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%I A059376
%S A059376 1,7,26,56,124,182,342,448,702,868,1330,1456,2196,2394,3224,3584,
%T A059376 4912,4914,6858,6944,8892,9310,12166,11648,15500,15372,18954,19152,
%U A059376 24388,22568,29790,28672,34580,34384,42408,39312,50652,48006,57096
%N A059376 Jordan function J_3(n).
%D A059376 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 199, #3.
%D A059376 R. Sivaramakrishnan, "The many facets of Euler's totient. II. Generalizations 
               and analogues", Nieuw Arch. Wisk. (4) 8 (1990), no. 2, 169-187.
%H A059376 T. D. Noe, <a href="b059376.txt">Table of n, a(n) for n=1..1000</a>
%F A059376 Multiplicative with a(p^e) = p^(3e)-p^(3e-3). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Jul 26 2001
%F A059376 a(n)=sum(d|n, d^3*mu(n/d)) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Apr 05 2002
%F A059376 Dirichlet generating function: zeta(s-3)/zeta(s). - Franklin T. Adams-Watters, 
               Sep 11 2005.
%p A059376 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 = 3)
%o A059376 (PARI) for(n=1,120,print1(sumdiv(n,d,d^3*moebius(n/d)),","))
%o A059376 (PARI) { for (n = 1, 1000, write("b059376.txt", n, " ", sumdiv(n, d, 
               d^3*moebius(n/d))); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Jun 26 2009]
%Y A059376 See A059379 and A059380 (triangle of values of J_k(n)), A000010 (J_1), 
               A059376 (J_3), A059377 (J_4), A059378 (J_5).
%Y A059376 Sequence in context: A063153 A063578 A063159 this_sequence A049453 A046433 
               A128972
%Y A059376 Adjacent sequences: A059373 A059374 A059375 this_sequence A059377 A059378 
               A059379
%K A059376 nonn,mult
%O A059376 1,2
%A A059376 N. J. A. Sloane (njas(AT)research.att.com), Jan 28 2001

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