%I #24 Sep 08 2022 08:45:56

%S 1,12,18,20,28,44,45,48,50,52,63,68,72,75,76,80,92,98,99,108,112,116,

%T 117,124,147,148,153,162,164,171,172,175,176,188,192,200,207,208,212,

%U 236,242,244,245,261,268,272,275,279,284,288,292,304,316,320,325,332

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

%C Numbers k such that A162641(k) = A162642(k). - _Amiram Eldar_, Sep 27 2021

%H Amiram Eldar, <a href="/A187039/b187039.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Zak Seidov)

%e 108 = 2^2*3^3 has one even and one odd exponent in its factorization and therefore qualifies.

%t 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 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 (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 Cf. A162641, A162642.

%K nonn

%O 1,2

%A _Vladimir Shevelev_, Mar 02 2011