

A350337


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


0



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
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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



FORMULA

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


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



KEYWORD

nonn


AUTHOR



STATUS

approved



