cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A144913 #17 Dec 26 2021 15:32:40
%S A144913 4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,324,400,441,484,
%T A144913 576,625,676,729,784,900,1024,1089,1225,1296,1521,1600,1764,1936,2025,
%U A144913 2304,2401,2500,2704,2916,3025,3136,3600,3969,4096,4225,4356,4900,5184,5625
%N A144913 Integers which are the product of even powers of primes up to 13.
%H A144913 Charles R Greathouse IV, <a href="/A144913/b144913.txt">Table of n, a(n) for n = 1..10000</a>
%F A144913 a(n) = A080197(n+1)^2. - _Rémy Sigrist_, Sep 26 2020
%F A144913 Sum_{n>=1} 1/a(n) = -1 + Product_{primes p <= 13} p^2/(p^2-1) = 273347/442368. - _Amiram Eldar_, Oct 14 2020
%t A144913 Select[ Range[75]^2, (fi = FactorInteger[#]; Max[ fi[[All, 1]] ] <= 13 && And @@ EvenQ /@ fi[[All, 2]]) &] (* _Jean-François Alcover_, Oct 10 2012 *)
%t A144913 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 *)
%o A144913 (PARI) is(n)=if(issquare(n,&n), my(f=factor(n)[,1]); #f && f[#f]<14, 0) \\ _Charles R Greathouse IV_, Jun 17 2013
%Y A144913 Subsequence of A000290 and A080197.
%Y A144913 Cf. A001694.
%K A144913 easy,nice,nonn
%O A144913 1,1
%A A144913 _Reikku Kulon_, Sep 25 2008, Sep 26 2008