A144913 Integers which are the product of even powers of primes up to 13.

4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 324, 400, 441, 484, 576, 625, 676, 729, 784, 900, 1024, 1089, 1225, 1296, 1521, 1600, 1764, 1936, 2025, 2304, 2401, 2500, 2704, 2916, 3025, 3136, 3600, 3969, 4096, 4225, 4356, 4900, 5184, 5625

Offset: 1

Author

Reikku Kulon, Sep 25 2008, Sep 26 2008

Keywords

• easy
• nice
• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A000290 and A080197.

Cf. A001694.

Programs

Mathematica

Select[ Range[75]^2, (fi = FactorInteger[#]; Max[ fi[[All, 1]] ] <= 13 && And @@ EvenQ /@ fi[[All, 2]]) &] (* Jean-François Alcover, Oct 10 2012 *)
eppQ[n_]:=Module[{fi=FactorInteger[n]},Max[fi[[All,1]]]<=13&&AllTrue[ fi[[All,2]],EvenQ]]; Select[Range[6000],eppQ] (* Harvey P. Dale, Dec 26 2021 *)

PARI

is(n)=if(issquare(n,&n), my(f=factor(n)[,1]); #f && f[#f]<14, 0) \\ Charles R Greathouse IV, Jun 17 2013

Formula

a(n) = A080197(n+1)^2. - Rémy Sigrist, Sep 26 2020

Sum_{n>=1} 1/a(n) = -1 + Product_{primes p <= 13} p^2/(p^2-1) = 273347/442368. - Amiram Eldar, Oct 14 2020