A175462 Number of divisors of integers of the form 5 + 8n.

2, 2, 4, 2, 2, 6, 2, 2, 4, 4, 4, 4, 2, 2, 6, 4, 4, 4, 2, 2, 8, 2, 2, 8, 2, 4, 4, 4, 2, 4, 6, 4, 6, 2, 2, 8, 2, 4, 4, 2, 6, 6, 4, 2, 8, 4, 2, 4, 2, 2, 10, 4, 2, 8, 4, 4, 4, 2, 4, 6, 4, 4, 4, 2, 4, 12, 4, 2, 6, 2, 4, 4, 4, 4, 4, 6, 2, 8, 4, 6, 8, 2, 2, 4, 2, 4, 12, 2, 2, 4, 6, 2, 8, 4, 2, 12, 2, 4, 4, 2, 8, 4, 2

Offset: 0

Author

Zak Seidov, May 23 2010

Keywords

• nonn
• easy

Comments

All terms are even.

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A004770 (Numbers of form 8n + 5), A007521 (Primes of form 8n + 5). A000005 (d(n) : number of divisors of n), A001620.

Programs

Maple

map(numtheory:-tau,[seq(i,i=5..1000,8)]); # Robert Israel, Mar 20 2020

Mathematica

Table[DivisorSigma[0, 8*n + 5], {n, 0, 100}] (* Amiram Eldar, Jan 14 2024 *)

PARI

a(n) = numdiv(5+8*n); \\ Michel Marcus, Oct 15 2013

Formula

a(n) = d(5 + 8*n).

a(n) = A000005(A004770(n)).

Sum_{k=1..n} a(k) ~ (n/2) * (log(n) + 2*gamma - 1 + 5*log(2)), where gamma is Euler's constant (A001620). - Amiram Eldar, Jan 14 2024