A114128 Numbers that factorize into a prime number of distinct prime factors each raised to a different prime exponent.

72, 108, 200, 288, 392, 500, 675, 800, 864, 968, 972, 1125, 1152, 1323, 1352, 1372, 1568, 1944, 2312, 2888, 3087, 3200, 3267, 3456, 3872, 4000, 4232, 4563, 5324, 5408, 6075, 6125, 6272, 6728, 7688, 7803, 8575, 8748, 8788, 9248, 9747, 10952, 10976

Offset: 1

Author

Jon Wild, Feb 14 2006

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..600

Crossrefs

Subsequence of A114129.

Programs

Mathematica

pnpfQ[n_]:=Module[{pn=PrimeNu[n],fi=Transpose[FactorInteger[n]][[2]]}, PrimeQ[ pn]&&Length[Union[fi]]==pn&&AllTrue[fi,PrimeQ]]; Select[Range[ 11000], pnpfQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 12 2015 *)

PARI

isok(n) = {nbf = omega(n); if (! isprime(nbf), return (0)); f = factor(n); for (i = 1, nbf, if (! isprime(f[i, 2]), return (0)); for (j = i+1, nbf, if (f[i, 2] == f[j, 2], return (0)););); return (1);} \\ Michel Marcus, Aug 18 2013

Extensions

Definition clarified by Harvey P. Dale, Aug 12 2015