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

1,1

Links

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

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

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 *)

Prog

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

Crossrefs

Subsequence of A000290 and A080197.

Cf. A001694.

Sequence in context: A253909 A305559 A221222 * A018885 A025741 A179459

Adjacent sequences: A144910 A144911 A144912 * A144914 A144915 A144916

Keyword

easy,nice,nonn

Author

Reikku Kulon, Sep 25 2008, Sep 26 2008

Status

approved