A273165 One half the number of divisors of nonprime numbers that are 3 (mod 4).

2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 2, 2, 2, 4, 2, 3, 2, 2, 3, 3, 2, 2, 4, 2, 3, 2, 2, 4, 2, 3, 2, 4, 2, 2, 3, 3, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 4, 2, 3, 2, 4, 3, 2, 2, 4, 2, 2, 2, 2, 3, 2, 4, 2, 2, 4, 4, 2, 3, 4, 6, 3, 2, 2, 2, 2, 3, 2, 3, 2, 2, 4, 2, 5, 3, 2

Offset

1,1

Comments

With the Jan 05 2004 Jovovic comment on A078703 a(n) is also the number of divisors +1 as well as -1 (mod 4) of A091236(n). See the example section of A273164.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000005(A091236(n))/2.

Sum_{k=1..n} a(k) ~ (log(n) + 2*gamma - 1 + 4*log(2))*n/4, where gamma is Euler's constant (A001620). - Amiram Eldar, Mar 10 2026

Mathematica

DivisorSigma[0, Select[4 * Range[0, 150] + 3, !PrimeQ[#] &]] / 2 (* Amiram Eldar, Mar 10 2026 *)

Prog

(PARI) list(lim) = apply(x -> numdiv(x)/2, select(x -> x%4 == 3 && !isprime(x), vector(lim, i, i))); \\ Amiram Eldar, Mar 10 2026

Crossrefs

Row lengths of A273164.

Cf. A000005, A001620, A078703, A091236.

Sequence in context: A212300 A165074 A374152 * A336313 A095139 A109038

Adjacent sequences: A273162 A273163 A273164 * A273166 A273167 A273168

Keyword

nonn,easy

Author

Wolfdieter Lang, Jul 29 2016

Extensions

Data corrected by Amiram Eldar, Mar 10 2026

Status

approved