A082050 Sum of divisors of n that are not of the form 3k+1.

0, 2, 3, 2, 5, 11, 0, 10, 12, 7, 11, 23, 0, 16, 23, 10, 17, 38, 0, 27, 24, 13, 23, 55, 5, 28, 39, 16, 29, 61, 0, 42, 47, 19, 40, 86, 0, 40, 42, 35, 41, 88, 0, 57, 77, 25, 47, 103, 0, 57, 71, 28, 53, 119, 16, 80, 60, 31, 59, 153, 0, 64, 96, 42, 70, 121, 0, 87, 95, 56, 71, 190

Offset

1,2

Links

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

Formula

a(A004611(n)) = 0.

G.f.: Sum_{k>=1} x^(2*k)*(2+3*x^k+x^(3*k))/(1-x^(3*k))^2. - Vladeta Jovovic, Apr 11 2006

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[(#-1)/3]&]]; Array[sd, 80] (* Harvey P. Dale, May 04 2011 *)

Prog

(PARI) for(n=1, 100, print1(sumdiv(n, d, if(d%3!=1, d))", "))
(PARI)
N = 66;  x = 'x + O('x^N);
gf = sum(n=1, N, (3*n-1)*x^(3*n-1)/(1-x^(3*n-1)) + (3*n)*x^(3*n)/(1-x^(3*n)) );
v = Vec(gf);  concat([0], v)
\\ Joerg Arndt, May 17 2013

Crossrefs

Cf. A000203, A004611, A027748, A046913, A078181, A078182, A082051, A086463.

Sequence in context: A335362 A371395 A059098 * A353956 A367633 A183098

Adjacent sequences: A082047 A082048 A082049 * A082051 A082052 A082053

Keyword

nonn,easy

Author

Ralf Stephan, Apr 02 2003

Status

approved