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

1,2

Comments

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

Links

Table of n, a(n) for n=1..73.

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A340316 A274608 A319680 * A133477 A303695 A345321

Adjacent sequences: A350334 A350335 A350336 * A350338 A350339 A350340

Keyword

nonn

Author

Wesley Ivan Hurt, Dec 25 2021

Status

approved