cp's OEIS Frontend

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

%I A177891 #16 Feb 17 2020 00:25:41
%S A177891 6,9,14,15,16,18,20,22,25,33,36,38,45,46,51,52,62,68,70,72,75,80,86,
%T A177891 87,91,93,95,99,104,105,110,116,117,118,119,130,136,141,142,143,144,
%U A177891 145,148,154,158,159,160,162,165,166,169,183,195,196,200
%N A177891 Numbers n such that sum of proper (or aliquot) divisors of n is a semiprime.
%C A177891 This is to A037020 as semiprimes A001358 are to primes A000040. The first four values are themselves semiprime.
%C A177891 Contains k^2 if k is in A005383. - _Robert Israel_, Feb 16 2020
%H A177891 Robert Israel, <a href="/A177891/b177891.txt">Table of n, a(n) for n = 1..10000</a>
%F A177891 A001065(a(n)) is in A001358.
%e A177891 a(2) = 9 because the aliquot divisors of 9 are 1 and 3, whose sum is 4 = 2*2, semiprime.
%e A177891 a(5) = 16 because the aliquot divisors of 16 are 1, 2, 4, and 8, whose sum is 15 = 3*5, semiprime.
%p A177891 filter:= proc(n) uses numtheory;
%p A177891   bigomega(sigma(n)-n) = 2
%p A177891 end proc:
%p A177891 select(filter, [$1..1000]); # _Robert Israel_, Feb 16 2020
%t A177891 semiPrimeQ[x_] := Plus @@ Last /@ FactorInteger@ x == 2; fQ[n_] := semiPrimeQ[ DivisorSigma[1, n] - n]; Select[ Range@ 200, fQ]
%o A177891 (PARI) isok(n) = bigomega(sigma(n)-n) == 2; \\ _Michel Marcus_, Apr 05 2015
%Y A177891 Cf. A001065, A001358, A005383, A037020.
%K A177891 nonn,easy
%O A177891 1,1
%A A177891 _Jonathan Vos Post_, Dec 14 2010