A326394 -id:A326394 - cp's OEIS frontend

A082051 Sum of divisors of n that are not of the form 3k+2.

1, 1, 4, 5, 1, 10, 8, 5, 13, 11, 1, 26, 14, 8, 19, 21, 1, 37, 20, 15, 32, 23, 1, 50, 26, 14, 40, 40, 1, 65, 32, 21, 37, 35, 8, 89, 38, 20, 56, 55, 1, 80, 44, 27, 73, 47, 1, 114, 57, 36, 55, 70, 1, 118, 56, 40, 80, 59, 1, 141, 62, 32, 104, 85, 14, 131, 68, 39, 73, 88, 1, 185

Offset: 1

Ralf Stephan, Apr 02 2003

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A000203, A003627, A027748, A046913, A078181, A078182, A082050, A086463, A326394.

sd[n_]:= Total[Select[Divisors[n], !IntegerQ[(# - 2) / 3]&]]; Array[sd, 100] (* Vincenzo Librandi, May 17 2013 *)

for(n=1,100,print1(sumdiv(n,d,if(d%3!=2,d))","))

N = 66;  x = 'x + O('x^N);
gf = sum(n=1,N, (3*n-2)*x^(3*n-2)/(1-x^(3*n-2)) + (3*n)*x^(3*n)/(1-x^(3*n)) );
v = Vec(gf)
\\ Joerg Arndt, May 17 2013

a(A003627(n)) = 1.
G.f.: Sum_{k>=1} x^k*(1 + 3*x^(2*k) + 2*x^(3*k))/(1 - x^(3*k))^2. - Ilya Gutkovskiy, Sep 12 2019
Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^2/18 = 0.548311... (A086463). - Amiram Eldar, Jan 06 2024

A326395 Expansion of Sum_{k>=1} x^(2k) (1 + x^k) / (1 - x^(3*k)).

Original entry on oeis.org

0, 1, 1, 1, 1, 3, 0, 2, 2, 2, 1, 4, 0, 2, 3, 2, 1, 5, 0, 3, 2, 2, 1, 6, 1, 2, 3, 2, 1, 6, 0, 3, 3, 2, 2, 7, 0, 2, 2, 4, 1, 6, 0, 3, 5, 2, 1, 7, 0, 3, 3, 2, 1, 7, 2, 4, 2, 2, 1, 9, 0, 2, 4, 3, 2, 6, 0, 3, 3, 4, 1, 10, 0, 2, 4, 2, 2, 6, 0, 5, 4, 2, 1, 8, 2, 2, 3, 4, 1, 10

Offset: 1

Ilya Gutkovskiy, Sep 11 2019

nonn

Number of divisors of n that are not of the form 3*k + 1.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000005, A001817, A001822, A004611 (positions of 0's), A007494, A035191, A082050, A326394.

Cf. A001620, A256425.

N:= 100: # for a(1) .. a(N)
S:= series(add(x^(2*k)*(1+x^k)/(1-x^(3*k)),k=1..N/2),x,N+1):
seq(coeff(S,x,i),i=1..N); # Robert Israel, Aug 27 2020

nmax = 90; CoefficientList[Series[Sum[x^(2 k) (1 + x^k)/(1 - x^(3 k)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
Table[DivisorSum[n, 1 &, !MemberQ[{1}, Mod[#, 3]] &], {n, 1, 90}]

a(n) = {numdiv(n) - sumdiv(n, d, d%3==1)} \\ Andrew Howroyd, Sep 11 2019

a(n) = A000005(n) - A001817(n).

Sum_{k=1..n} a(k) ~ 2*n*log(n)/3 + c*n, where c = (5*gamma-2)/3 - gamma(1,3) = (5*A001620-2)/3 - A256425 = -0.382447... . - Amiram Eldar, Jan 14 2024

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A082051 Sum of divisors of n that are not of the form 3k+2.

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A326395 Expansion of Sum_{k>=1} x^(2k) (1 + x^k) / (1 - x^(3*k)).

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cp's OEIS Frontend

A082051 Sum of divisors of n that are not of the form 3k+2.

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A326395 Expansion of Sum_{k>=1} x^(2*k) * (1 + x^k) / (1 - x^(3*k)).

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Maple

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A326395 Expansion of Sum_{k>=1} x^(2k) (1 + x^k) / (1 - x^(3*k)).