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A114129 Numbers that factorize into a set of prime factors that are each raised to a different prime exponent. 6
4, 8, 9, 25, 27, 32, 49, 72, 108, 121, 125, 128, 169, 200, 243, 288, 289, 343, 361, 392, 500, 529, 675, 800, 841, 864, 961, 968, 972, 1125, 1152, 1323, 1331, 1352, 1369, 1372, 1568, 1681, 1849, 1944, 2048, 2187, 2197, 2209, 2312, 2809, 2888, 3087, 3125, 3200 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

MATHEMATICA

dpeQ[n_]:=Module[{exps=Transpose[FactorInteger[n]][[2]]}, CompositeQ[n] && Length[ Union[exps]]==Length[exps]&&AllTrue[exps, PrimeQ]]; Select[ Range[ 3500], dpeQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 02 2016 *)

PROG

(PARI) isok(n) = {nbf = omega(n); 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

(PARI) is(n)=if(n<4, return(0)); my(f=factor(n)[, 2]); vecmin(apply(isprime, f)) && #Set(f)==#f \\ Charles R Greathouse IV, Sep 08 2016

CROSSREFS

Subsequence of A130091.

Sequence in context: A056166 A093771 A051676 * A053810 A076702 A051761

Adjacent sequences:  A114126 A114127 A114128 * A114130 A114131 A114132

KEYWORD

nonn

AUTHOR

Jon Wild, Feb 14 2006

STATUS

approved

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Last modified April 6 10:05 EDT 2020. Contains 333273 sequences. (Running on oeis4.)