A114129 Numbers that factorize into a set of prime factors that are each raised to a different prime exponent.

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

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: A093771 A371223 A051676 * A053810 A076702 A051761

Adjacent sequences: A114126 A114127 A114128 * A114130 A114131 A114132

Keyword

nonn

Author

Jon Wild, Feb 14 2006

Status

approved