A175462 - OEIS

%I #15 Jan 14 2024 02:25:21

%S 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,

%T 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,

%U 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

%N Number of divisors of integers of the form 5 + 8n.

%C All terms are even.

%H Robert Israel, <a href="/A175462/b175462.txt">Table of n, a(n) for n = 0..10000</a>

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

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

%F 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

%p map(numtheory:-tau,[seq(i,i=5..1000,8)]); # _Robert Israel_, Mar 20 2020

%t Table[DivisorSigma[0, 8*n + 5], {n, 0, 100}] (* _Amiram Eldar_, Jan 14 2024 *)

%o (PARI) a(n) = numdiv(5+8*n); \\ _Michel Marcus_, Oct 15 2013

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

%K nonn,easy

%O 0,1

%A _Zak Seidov_, May 23 2010