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A293376 Corresponding values of pod(n)/tau(n) of numbers n from A120736.

%I A293376 #14 Apr 29 2025 17:20:24
%S A293376 1,1,9,16,9,25,288,49,972,121,41472,169,101250,289,1119744,361,320000,
%T A293376 388962,529,1062882,1229312,841,3888000000,961,2371842,3001250,
%U A293376 11609505792,1369,4626882,327680000,1681,29274835968,1849,7496192,44286750000,2209,65229815808
%N A293376 Corresponding values of pod(n)/tau(n) of numbers n from A120736.
%C A293376 Integer of pod(n)/tau(n) of numbers n such that tau(n) = the number of the divisors of n (A000005) divides pod(n) = the product of the divisors of n (A007955).
%H A293376 Jaroslav Krizek, <a href="/A293376/b293376.txt">Table of n, a(n) for n = 1..1000</a>
%F A293376 a(n) = A291186(A120736(n))/A137927(A120736(n)).
%e A293376 For n = 3; A120736(3) = 6; pod(6)/tau(6) = 36/4 = 9.
%t A293376 (Times @@ #)/Length@ # &@ Divisors@ # & /@ Select[Range@ 100, Divisible[Times @@ Divisors@ #, DivisorSigma[0, #]] &] (* _Michael De Vlieger_, Oct 10 2017 *)
%o A293376 (Magma) [Numerator(&*[d: d in Divisors(n)] / #[d: d in Divisors(n)]): n in [1..1000] | Denominator(&*[d: d in Divisors(n)] / #[d: d in Divisors(n)]) eq 1];
%Y A293376 Cf. A000005, A007955, A120736, A137927, A291186.
%K A293376 nonn
%O A293376 1,3
%A A293376 _Jaroslav Krizek_, Oct 07 2017