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

1,3

Links

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A201411 A353313 A206282 * A196848 A369950 A266699

Adjacent sequences: A082048 A082049 A082050 * A082052 A082053 A082054

Keyword

nonn,easy

Author

Ralf Stephan, Apr 02 2003

Status

approved