A359290 Number of divisors of 4*n-2 of form 4*k+3.

0, 1, 0, 1, 1, 1, 0, 2, 0, 1, 2, 1, 0, 2, 0, 1, 2, 2, 0, 2, 0, 1, 2, 1, 1, 2, 0, 2, 2, 1, 0, 3, 0, 1, 2, 1, 0, 3, 2, 1, 2, 1, 0, 2, 0, 2, 2, 2, 0, 3, 0, 1, 4, 1, 0, 2, 0, 2, 2, 2, 1, 2, 0, 1, 2, 1, 2, 4, 0, 1, 2, 2, 0, 3, 0, 1, 2, 2, 0, 2, 2, 1, 4, 1, 0, 3, 0, 3, 2, 1

Offset: 1

Author

Seiichi Manyama, Dec 24 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001842, A078703, A359240.

Programs

Mathematica

Table[Count[Divisors[4 n-2],?(IntegerQ[(#-3)/4]&)],{n,100}] (* _Harvey P. Dale, May 09 2023 *)
a[n_] := DivisorSum[4*n-2, 1 &, Mod[#, 4] == 3 &]; Array[a, 100] (* Amiram Eldar, Aug 16 2023 *)

PARI

a(n) = sumdiv(4*n-2, d, d%4==3);

PARI

my(N=100, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(2*k)/(1-x^(4*k-1)))))

PARI

my(N=100, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(3*k-1)/(1-x^(4*k-2)))))

Formula

a(n) = A001842(4*n-2).

G.f.: Sum_{k>0} x^(2*k)/(1 - x^(4*k-1)).

G.f.: Sum_{k>0} x^(3*k-1)/(1 - x^(4*k-2)).