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

Author

Jon Wild, Feb 14 2006

Keywords

• nonn

Links

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

Crossrefs

Subsequence of A130091.

Programs

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 *)

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