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

1,1

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

Links

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

Amritpal Singh, c++ program for generating the sequence

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000005, A006881. Contains A030515.

Sequence in context: A263189 A263838 A217856 * A030515 A162947 A351201

Adjacent sequences: A253385 A253386 A253387 * A253389 A253390 A253391

Keyword

nonn

Author

Amritpal Singh, Dec 31 2014

Status

approved