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A240502 Product of primes appearing in the factorization of n! with even exponents.

%I A240502 #24 Feb 24 2023 10:28:34
%S A240502 1,1,1,1,1,1,6,6,3,3,30,30,10,10,35,21,21,21,42,42,210,10,55,55,330,
%T A240502 330,2145,715,5005,5005,6006,6006,3003,91,3094,2210,2210,2210,20995,
%U A240502 4845,1938,1938,2261,2261,24871,124355,5720330,5720330,17160990,17160990,8580495
%N A240502 Product of primes appearing in the factorization of n! with even exponents.
%C A240502 All terms are squarefree (A005117). - _Michel Marcus_, Feb 15 2016
%H A240502 David A. Corneth, <a href="/A240502/b240502.txt">Table of n, a(n) for n = 0..7585</a>
%F A240502 a(n) = rad(n!)/core(n!) = A336643(n!). - _Benoit Cloitre_, Mar 12 2022
%e A240502 In the prime power factorization 2^7*3^4*5*7 of 9! only the exponent of 3 is even. Thus a(9)=3.
%t A240502 Table[Times@@Select[FactorInteger[n!],EvenQ[#[[2]]]&][[;;,1]],{n,0,50}] (* _Harvey P. Dale_, Feb 24 2023 *)
%o A240502 (PARI) a(n) = {my(f = factor(n!)); for (k=1, #f~, f[k, 2] = 1 - (f[k, 2] % 2);); factorback(f);} \\ _Michel Marcus_, Feb 15 2016
%o A240502 (PARI) a(n) = {my(res=1); forprime(p=2, n\2, e=val(n,p); if(e%2==0,res*=p)); res}
%o A240502 val(n, p) = my(r=0); while(n, r+=n\=p); r \\ _David A. Corneth_, Feb 24 2023
%Y A240502 Cf. A000142, A005117, A055204.
%K A240502 nonn
%O A240502 0,7
%A A240502 _Vladimir Shevelev_, Apr 06 2014
%E A240502 More terms from _Michel Marcus_, Feb 15 2016