A177425 Integers with multiple and strictly distinct powers.

12, 18, 20, 24, 28, 40, 44, 45, 48, 50, 52, 54, 56, 63, 68, 72, 75, 76, 80, 88, 92, 96, 98, 99, 104, 108, 112, 116, 117, 124, 135, 136, 144, 147, 148, 152, 153, 160, 162, 164, 171, 172, 175, 176, 184, 188, 189, 192, 200, 207, 208, 212, 224, 232, 236, 242, 244, 245

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 07 2010

Keywords

• nonn
• easy

Comments

12=2^2*3, 18=2*3^2,.. 600=2^3*3*5^2,..

Links

• Lei Zhou, Table of n, a(n) for n = 1..10000

Crossrefs

Apart from its first term, A001749 is a subsequence.

Cf. A001358.

Programs

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]];lst={};Do[If[Length[f[n]]>1&&f[n]==Union@f[n],AppendTo[lst,n]],{n,0,6!}];lst

PARI

is(n)=my(f=vecsort(factor(n)[,2]~)); n>1 && Set(f)==f && #f>1 \\ Charles R Greathouse IV, Mar 20 2014

Formula

a(n) << n log n. - Charles R Greathouse IV, Mar 25 2014