Search: id:A033196
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%I A033196
%S A033196 1,12,36,96,150,432,392,768,972,1800,1452,3456,2366,4704,5400,6144,
%T A033196 5202,11664,7220,14400,14112,17424,12696,27648,18750,28392,26244,
%U A033196 37632,25230,64800,30752,49152,52272,62424,58800,93312,52022,86640
%N A033196 n^3*Product_{p|n} (1 + 1/p).
%H A033196 T. D. Noe, <a href="b033196.txt">Table of n, a(n) for n=1..1000</a>
%F A033196 Dirichlet g.f.: zeta(s-2)*zeta(s-3)/zeta(2*s-4).
%F A033196 Multiplicative with a(p^e) = p^e*p^(2*e-1)*(p+1). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Nov 16 2001
%F A033196 a(n)=sum_{d|n} mu(d)*sigma(n^3/d^2)=n^2*A001615(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Feb 16 2008
%o A033196 (PARI) a(n)=direuler(p=2,n,(1+p^2*X)/(1-p^3*X))[n]
%o A033196 (PARI) a(n)=sumdiv(n,d,moebius(d)*sigma(n^3/d^2)) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Feb 16 2008
%Y A033196 a(n)=n^2*A001615(n). Cf. A000082.
%Y A033196 Sequence in context: A049598 A152135 A080562 this_sequence A060621 A058880 
               A055551
%Y A033196 Adjacent sequences: A033193 A033194 A033195 this_sequence A033197 A033198 
               A033199
%K A033196 nonn,easy,mult
%O A033196 1,2
%A A033196 N. J. A. Sloane (njas(AT)research.att.com).
%E A033196 Additional comments from Michael Somos, May 19, 2000.

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