%I #19 Sep 05 2024 19:14:06
%S 1,1,3,8,5,9,7,16,9,25,11,288,13,49,225,1024,17,972,19,4000,441,121,
%T 23,41472,125,169,729,10976,29,101250,31,16384,1089,289,1225,1119744,
%U 37,361,1521,320000,41,388962,43,42592,30375,529,47,127401984,343,62500,2601
%N a(n) = numerator of (pod(n) / tau(n)).
%C pod(n) = the product of the divisors of n (A007955), tau(n) = the number of the divisors of n (A000005).
%H Robert Israel, <a href="/A291186/b291186.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = numerator of (A007955(n) / A000005(n)).
%e For n = 4; pod(4) / tau(4) = 8 / 3; a(n) = 8.
%p f:= proc(n) local D; D:= numtheory:-divisors(n); numer(convert(D,`*`)/nops(D)) end proc:
%p map(f, [$1..100]); # _Robert Israel_, Sep 14 2017
%t Table[Numerator[Apply[Times, Divisors@ n]/DivisorSigma[0, n]], {n, 51}] (* _Michael De Vlieger_, Sep 05 2017 *)
%o (Magma) [Numerator(&*[d: d in Divisors(n)] / #[d: d in Divisors(n)]): n in [1..1000]];
%o (PARI) a(n) = my(d=divisors(n)); numerator(prod(k=1, #d, d[k])/#d); \\ _Michel Marcus_, Sep 05 2017
%Y Cf. A137927 (denominator).
%Y Cf. A000005, A007955, A120736.
%K nonn,frac
%O 1,3
%A _Jaroslav Krizek_, Sep 05 2017