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

1,1

Links

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

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 *)

Prog

(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

Crossrefs

Subsequence of A114129.

Sequence in context: A272191 A072412 A052486 * A143610 A166987 A339940

Adjacent sequences: A114125 A114126 A114127 * A114129 A114130 A114131

Keyword

nonn

Author

Jon Wild, Feb 14 2006

Extensions

Definition clarified by Harvey P. Dale, Aug 12 2015

Status

approved