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Search: id:A046913
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| A046913 |
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Sum of divisors of n not congruent to 0 mod 3. |
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+0
7
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| 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, 42, 1, 56, 30, 18, 32, 63, 12, 54, 48, 7, 38, 60, 14, 90, 42, 24, 44, 84, 6, 72, 48, 31, 57, 93, 18, 98, 54, 3, 72, 120, 20, 90, 60, 42, 62, 96, 8, 127, 84, 36, 68, 126
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also a(n)=A000203[3n]-3A000203[n]. - Labos E. (labos(AT)ana.sote.hu), Aug 14 2003
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
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FORMULA
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Multiplicative with a(3^e) = 1, a(p^e) = (p^(e+1)-1)/(p-1) for p<>3. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 11 2002
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.yu), Dec 18 2002
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
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EXAMPLE
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Divisors of 12 are 1 2 3 4 6 12, and discarding 3 6 and 12 we get a(12)=1+2+4=7.
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MATHEMATICA
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Table[DivisorSigma[1, 3*w]-3*DivisorSigma[1, w], {w, 1, 256}]
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PROGRAM
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(PARI) a(n)=if(n<1, 0, sigma(3*n)-3*sigma(n)) /* Michael Somos, Jul 19 2004 */
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CROSSREFS
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Cf. A035191.
Cf. A051731, A091684.
Sequence in context: A111806 A054458 A110168 this_sequence A118228 A082053 A136035
Adjacent sequences: A046910 A046911 A046912 this_sequence A046914 A046915 A046916
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KEYWORD
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nonn,mult
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AUTHOR
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njas
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