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.

A187039 Numbers that have equal counts of even and odd exponents of primes in their factorization.

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%I A187039 #24 Sep 08 2022 08:45:56
%S A187039 1,12,18,20,28,44,45,48,50,52,63,68,72,75,76,80,92,98,99,108,112,116,
%T A187039 117,124,147,148,153,162,164,171,172,175,176,188,192,200,207,208,212,
%U A187039 236,242,244,245,261,268,272,275,279,284,288,292,304,316,320,325,332
%N A187039 Numbers that have equal counts of even and odd exponents of primes in their factorization.
%C A187039 Numbers k such that A162641(k) = A162642(k). - _Amiram Eldar_, Sep 27 2021
%H A187039 Amiram Eldar, <a href="/A187039/b187039.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Zak Seidov)
%e A187039 108 = 2^2*3^3 has one even and one odd exponent in its factorization and therefore qualifies.
%t A187039 Reap[Do[fi=FactorInteger[n];la=Mod[Last/@fi,2];If[Count[la,1]==Count[la,0],Sow[n]] ,{n,1,10000}]][[2,1]] (* _Zak Seidov_, Mar 04 2011 *)
%t A187039 eoeQ[n_]:=Module[{f=FactorInteger[n][[All,2]]},Count[ f,_?OddQ]== Length[ f]/2]; Join[{1},Select[Range[400],eoeQ]] (* _Harvey P. Dale_, Sep 23 2016 *)
%o A187039 (Magma) IsA187039:=func< n | #[ a: a in P | IsEven(a) ] eq #[ a: a in P | IsOdd(a) ] where P is [ g[2]: g in F ] where F is Factorization(n) >; [ n: n in [1..500] | IsA187039(n) ]; // _Klaus Brockhaus_, Mar 04 2011
%Y A187039 Cf. A162641, A162642.
%K A187039 nonn
%O A187039 1,2
%A A187039 _Vladimir Shevelev_, Mar 02 2011