A177891 Numbers n such that sum of proper (or aliquot) divisors of n is a semiprime.

6, 9, 14, 15, 16, 18, 20, 22, 25, 33, 36, 38, 45, 46, 51, 52, 62, 68, 70, 72, 75, 80, 86, 87, 91, 93, 95, 99, 104, 105, 110, 116, 117, 118, 119, 130, 136, 141, 142, 143, 144, 145, 148, 154, 158, 159, 160, 162, 165, 166, 169, 183, 195, 196, 200

Offset: 1

Author

Jonathan Vos Post, Dec 14 2010

Keywords

• nonn
• easy

Comments

This is to A037020 as semiprimes A001358 are to primes A000040. The first four values are themselves semiprime.

Contains k^2 if k is in A005383. - Robert Israel, Feb 16 2020

Examples

			a(2) = 9 because the aliquot divisors of 9 are 1 and 3, whose sum is 4 = 2*2, semiprime.
a(5) = 16 because the aliquot divisors of 16 are 1, 2, 4, and 8, whose sum is 15 = 3*5, semiprime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001065, A001358, A005383, A037020.

Programs

Maple

filter:= proc(n) uses numtheory;
  bigomega(sigma(n)-n) = 2
end proc:
select(filter, [$1..1000]); # Robert Israel, Feb 16 2020

Mathematica

semiPrimeQ[x_] := Plus @@ Last /@ FactorInteger@ x == 2; fQ[n_] := semiPrimeQ[ DivisorSigma[1, n] - n]; Select[ Range@ 200, fQ]

PARI

isok(n) = bigomega(sigma(n)-n) == 2; \\ Michel Marcus, Apr 05 2015

Formula

A001065(a(n)) is in A001358.