Search: id:A046913
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%I A046913
%S A046913 1,3,1,7,6,3,8,15,1,18,12,7,14,24,6,31,18,3,20,42,8,36,24,15,31,
%T A046913 42,1,56,30,18,32,63,12,54,48,7,38,60,14,90,42,24,44,84,6,72,48,
%U A046913 31,57,93,18,98,54,3,72,120,20,90,60,42,62,96,8,127,84,36,68,126
%N A046913 Sum of divisors of n not congruent to 0 mod 3.
%C A046913 Also a(n)=A000203[3n]-3A000203[n]. - Labos E. (labos(AT)ana.sote.hu), 
               Aug 14 2003
%C A046913 G.f. A(x) satisfies 0=f(A(x),A(x^2),A(x^4)) where f(u,v,w)=u^2+9v^2+16w^2-6uv+4uw-24vw-v+w. 
               - Michael Somos, Jul 19 2004
%F A046913 Multiplicative with a(3^e) = 1, a(p^e) = (p^(e+1)-1)/(p-1) for p<>3. 
               - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 11 2002
%F A046913 G.f.: Sum_{k>0} x^k*(1+2*x^k+2*x^(3*k)+x^(4*k))/(1-x^(3*k))^2. - Vladeta 
               Jovovic (vladeta(AT)eunet.rs), Dec 18 2002
%F A046913 Equals A051731 * A091684, where A051731 = the inverse Mobius transform 
               and A091684 = count with 3*n = 0: (1, 2, 0, 4, 5, 0, 7,...). Example: 
               a(4) = 7 = (1, 1, 0, 1) dot (1, 2, 0, 4) = (1 + 2 + 0 + 4), where 
               (1, 1, 0, 1) = row 4 of A051731. - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Jul 03 2008
%e A046913 Divisors of 12 are 1 2 3 4 6 12 and discarding 3 6 and 12 we get a(12)=1+2+4=7.
%t A046913 Table[DivisorSigma[1, 3*w]-3*DivisorSigma[1, w], {w, 1, 256}]
%o A046913 (PARI) a(n)=if(n<1,0,sigma(3*n)-3*sigma(n)) /* Michael Somos, Jul 19 
               2004 */
%Y A046913 Cf. A035191.
%Y A046913 Cf. A051731, A091684.
%Y A046913 Sequence in context: A111806 A054458 A110168 this_sequence A118228 A082053 
               A136035
%Y A046913 Adjacent sequences: A046910 A046911 A046912 this_sequence A046914 A046915 
               A046916
%K A046913 nonn,mult
%O A046913 1,2
%A A046913 N. J. A. Sloane (njas(AT)research.att.com).

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