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

Author

Ralf Stephan, Apr 02 2003

Keywords

• nonn
• easy

Links

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

Crossrefs

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

Programs

Mathematica

sd[n_]:=Total[Select[Divisors[n],!IntegerQ[(#-1)/3]&]]; Array[sd,80] (* Harvey P. Dale, May 04 2011 *)

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

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