A253388 Numbers n such that the number of divisors of n is the product of two distinct primes.

12, 18, 20, 28, 32, 44, 45, 48, 50, 52, 63, 68, 75, 76, 80, 92, 98, 99, 112, 116, 117, 124, 144, 147, 148, 153, 162, 164, 171, 172, 175, 176, 188, 192, 207, 208, 212, 236, 242, 243, 244, 245, 261, 268, 272, 275, 279, 284, 292, 304, 316, 320, 324, 325, 332, 333

Offset: 1

Author

Amritpal Singh, Dec 31 2014

Keywords

• nonn

Comments

n such that A000005(n) is in A006881.

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

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Amritpal Singh, c++ program for generating the sequence

Crossrefs

Cf. A000005, A006881. Contains A030515.

Programs

Maple

filter:= proc(n) local F;
  F:= ifactors(numtheory:-tau(n))[2];
  nops(F)=2 and F[1,2]=1 and F[2,2]=1;
end proc:
select(filter, [$1..1000]); # Robert Israel, Dec 31 2014

Mathematica

a253388Q[x_] := Block[{d = FactorInteger[DivisorSigma[0, x]]},
Length[d] == 2 && Max[Last@Transpose@d] == 1]; a253388[n_] := Select[Range@n, a253388Q]; a253388[333] (* Michael De Vlieger, Jan 02 2015 *)
fQ[x_] := PrimeOmega@ x == 2 == PrimeNu@ x; Select[ Range@ 250, fQ[ DivisorSigma[0, #]] &] (* Robert G. Wilson v, Jan 13 2015 *)

PARI

isok(n) = (nbd = numdiv(n)) && (omega(nbd) == 2) && (bigomega(nbd) == 2); \\ Michel Marcus, Feb 07 2015