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A078708
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Sum of divisors d of n such that n/d is not congruent to 0 mod 3.
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11
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1, 3, 3, 7, 6, 9, 8, 15, 9, 18, 12, 21, 14, 24, 18, 31, 18, 27, 20, 42, 24, 36, 24, 45, 31, 42, 27, 56, 30, 54, 32, 63, 36, 54, 48, 63, 38, 60, 42, 90, 42, 72, 44, 84, 54, 72, 48, 93, 57, 93, 54, 98, 54, 81, 72, 120, 60, 90, 60, 126, 62, 96, 72, 127, 84, 108, 68, 126, 72, 144
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: Sum_{k>0} x^k*(1+x^k)^2*(1+x^(2*k))/(1-x^(3*k))^2.
G.f.: Sum_{k>=1} k*x^k*(1 + x^k)/(1 - x^(3*k)). - Ilya Gutkovskiy, Sep 13 2019
Multiplicative with a(3^e) = 3^e and a(p^e) = (p^(e+1)-1)/(p-1) if p != 3.
Sum_{k=1..n} a(k) ~ c * n^2, where c = 2*Pi^2/27 = 0.731081... (A346933). (End)
Dirichlet g.f.: zeta(s)*zeta(s-1)*(1-1/3^s). - Amiram Eldar, Dec 30 2022
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MATHEMATICA
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f[p_, e_] := If[p == 3, 3^e, (p^(e+1)-1)/(p-1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 30 2022 *)
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PROG
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(PARI) for(n=1, 70, d=divisors(n); s=0; for(j=1, matsize(d)[2], if((n/d[j])%3>0, s=s+d[j])); print1(s, ", "))
(PARI) a(n)=sumdiv(n, d, if((n/d)%3, 1, 0)*d)
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CROSSREFS
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KEYWORD
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mult,easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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