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A114128 Numbers that factorize into a prime number of distinct prime factors each raised to a different prime exponent. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A251124

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

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Last modified January 17 18:14 EST 2020. Contains 330987 sequences. (Running on oeis4.)