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A253388 Numbers n such that the number of divisors of n is the product of two distinct primes. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A070011

Adjacent sequences:  A253385 A253386 A253387 * A253389 A253390 A253391

KEYWORD

nonn

AUTHOR

Amritpal Singh, Dec 31 2014

STATUS

approved

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Last modified July 14 18:26 EDT 2020. Contains 335729 sequences. (Running on oeis4.)