A253388 - OEIS

%I #30 Mar 29 2015 12:04:17

%S 12,18,20,28,32,44,45,48,50,52,63,68,75,76,80,92,98,99,112,116,117,

%T 124,144,147,148,153,162,164,171,172,175,176,188,192,207,208,212,236,

%U 242,243,244,245,261,268,272,275,279,284,292,304,316,320,324,325,332,333

%N Numbers n such that the number of divisors of n is the product of two distinct primes.

%C n such that A000005(n) is in A006881.

%C n is either of the form p^k where p is prime and k+1 is in A006881 or p1^k1*p2^k2 where p1 and p2 are distinct primes and k1+1 and k2+1 are distinct primes. - _Robert Israel_, Dec 31 2014

%H Robert Israel, <a href="/A253388/b253388.txt">Table of n, a(n) for n = 1..10000</a>

%H Amritpal Singh, <a href="/A253388/a253388_1.cpp.txt">c++ program for generating the sequence</a>

%e 12 has 6 divisors, and 6 is the product of two distinct primes, 2 and 3.

%p filter:= proc(n) local F;

%p   F:= ifactors(numtheory:-tau(n))[2];

%p   nops(F)=2 and F[1,2]=1 and F[2,2]=1;

%p end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Dec 31 2014

%t a253388Q[x_] := Block[{d = FactorInteger[DivisorSigma[0, x]]},

%t Length[d] == 2 && Max[Last@Transpose@d] == 1]; a253388[n_] := Select[Range@n, a253388Q]; a253388[333] (* _Michael De Vlieger_, Jan 02 2015 *)

%t fQ[x_] := PrimeOmega@ x == 2 == PrimeNu@ x; Select[ Range@ 250, fQ[ DivisorSigma[0, #]] &] (* _Robert G. Wilson v_, Jan 13 2015 *)

%o (PARI) isok(n) = (nbd = numdiv(n)) && (omega(nbd) == 2) && (bigomega(nbd) == 2); \\ _Michel Marcus_, Feb 07 2015

%Y Cf. A000005, A006881. Contains A030515.

%K nonn

%O 1,1

%A _Amritpal Singh_, Dec 31 2014