A350337 Sum of the divisors of n that are prime or the product of 2 (not necessarily distinct) primes.

0, 2, 3, 6, 5, 11, 7, 6, 12, 17, 11, 15, 13, 23, 23, 6, 17, 20, 19, 21, 31, 35, 23, 15, 30, 41, 12, 27, 29, 41, 31, 6, 47, 53, 47, 24, 37, 59, 55, 21, 41, 53, 43, 39, 32, 71, 47, 15, 56, 42, 71, 45, 53, 20, 71, 27, 79, 89, 59, 45, 61, 95, 40, 6, 83, 77, 67, 57, 95, 73, 71, 24, 73

Offset: 1

Author

Wesley Ivan Hurt, Dec 25 2021

Keywords

• nonn

Comments

Sum of the divisors of n of the form p, p^2, or p*q, where p and q are prime.

Crossrefs

Cf. A008472, A010051, A037143, A064911, A076290, A350331.

Programs

Mathematica

a[n_] := DivisorSum[n, # &, 0 < PrimeOmega[#] <= 2 &]; Array[a, 100] (* Amiram Eldar, Dec 26 2021 *)

PARI

a(n) = sumdiv(n, d, if (isprime(d) || (bigomega(d)==2), d)); \\ Michel Marcus, Dec 26 2021

Formula

a(n) = Sum_{d|n} d * (u(d) + v(d)), where u is the prime characteristic and v is the semiprime characteristic.

a(n) = A008472(n) + A076290(n). - Wesley Ivan Hurt, Jan 02 2024