A177891 - OEIS

%I #16 Feb 17 2020 00:25:41

%S 6,9,14,15,16,18,20,22,25,33,36,38,45,46,51,52,62,68,70,72,75,80,86,

%T 87,91,93,95,99,104,105,110,116,117,118,119,130,136,141,142,143,144,

%U 145,148,154,158,159,160,162,165,166,169,183,195,196,200

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

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

%C Contains k^2 if k is in A005383. - _Robert Israel_, Feb 16 2020

%H Robert Israel, <a href="/A177891/b177891.txt">Table of n, a(n) for n = 1..10000</a>

%F A001065(a(n)) is in A001358.

%e a(2) = 9 because the aliquot divisors of 9 are 1 and 3, whose sum is 4 = 2*2, semiprime.

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

%p filter:= proc(n) uses numtheory;

%p   bigomega(sigma(n)-n) = 2

%p end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Feb 16 2020

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

%o (PARI) isok(n) = bigomega(sigma(n)-n) == 2; \\ _Michel Marcus_, Apr 05 2015

%Y Cf. A001065, A001358, A005383, A037020.

%K nonn,easy

%O 1,1

%A _Jonathan Vos Post_, Dec 14 2010