Search: id:A059377
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%I A059377
%S A059377 1,15,80,240,624,1200,2400,3840,6480,9360,14640,19200,28560,36000,
%T A059377 49920,61440,83520,97200,130320,149760,192000,219600,279840,307200,
%U A059377 390000,428400,524880,576000,707280,748800,923520,983040,1171200
%N A059377 Jordan function J_4(n).
%C A059377 This sequence is multiplicative. - Mitch Harris, Apr 19 2005
%D A059377 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 199, #3.
%D A059377 R. Sivaramakrishnan, "The many facets of Euler's totient. II. Generalizations 
               and analogues", Nieuw Arch. Wisk. (4) 8 (1990), no. 2, 169-187.
%H A059377 T. D. Noe, <a href="b059377.txt">Table of n, a(n) for n=1..1000</a>
%F A059377 a(n)=sum(d|n, d^4*mu(n/d)) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Apr 05 2002
%F A059377 Multiplicative with a(p^e) = p^(4e)-p^(4(e-1)).
%F A059377 Dirichlet generating function: zeta(s-4)/zeta(s). - Franklin T. Adams-Watters, 
               Sep 11 2005.
%p A059377 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 = 4)
%o A059377 (PARI) for(n=1,100,print1(sumdiv(n,d,d^4*moebius(n/d)),","))
%o A059377 (PARI) a(n)=if(n<1,0,sumdiv(n,d,d^4*moebius(n/d)))
%o A059377 (PARI) a(n)=if(n<1,0,dirdiv(vector(n,k,k^4),vector(n,k,1))[n])
%o A059377 (PARI) { for (n = 1, 1000, write("b059377.txt", n, " ", sumdiv(n, d, 
               d^4*moebius(n/d))); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Jun 26 2009]
%Y A059377 See A059379 and A059380 (triangle of values of J_k(n)), A000010 (J_1), 
               A059376 (J_3), A059377 (J_4), A059378 (J_5).
%Y A059377 See A059379 and A059380 (triangle of values of J_k(n)), A000010 (J_1), 
               A007434 (J_2), A059376 (J_3), A059378 (J_5).
%Y A059377 Sequence in context: A082540 A085808 A033594 this_sequence A123865 A024002 
               A050149
%Y A059377 Adjacent sequences: A059374 A059375 A059376 this_sequence A059378 A059379 
               A059380
%K A059377 nonn,mult
%O A059377 1,2
%A A059377 N. J. A. Sloane (njas(AT)research.att.com), Jan 28 2001

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