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A378183 a(n) = rad(n)^binomial(omega(n) + bigomega(n) - 1, bigomega(n) - 2), where rad = A007947, bigomega = A001222, and omega = A001221.

%I A378183 #5 Nov 24 2024 09:39:16
%S A378183 1,1,1,2,1,6,1,8,3,10,1,1296,1,14,15,64,1,1296,1,10000,21,22,1,
%T A378183 60466176,5,26,27,38416,1,24300000,1,1024,33,34,35,60466176,1,38,39,
%U A378183 10000000000,1,130691232,1,234256,50625,46,1,3656158440062976,7,10000,51,456976,1
%N A378183 a(n) = rad(n)^binomial(omega(n) + bigomega(n) - 1, bigomega(n) - 2), where rad = A007947, bigomega = A001222, and omega = A001221.
%H A378183 Michael De Vlieger, <a href="/A378183/b378183.txt">Table of n, a(n) for n = 1..3359</a>
%F A378183 a(n) = A377379(n)/A377073(n).
%F A378183 For prime p, a(p) = 1.
%F A378183 For prime power p^k, a(p^k) = A243103(p^k)/p^k = A007955(p^k)/p^k = p^(k*(k-1)).
%F A378183 For n in A024619, a(n) != A243103(n).
%F A378183 For squarefree semiprime n (in A006881), a(n) = n.
%t A378183 Table[Apply[Times, #1]^Binomial[Length[#1] + Total[#2] - 1, Total[#2] - 2] & @@
%t A378183   Transpose@ FactorInteger[n], {n, 120}]
%Y A378183 Cf. A001221, A001222, A006881, A007947, A007955, A024619, A243103, A377379, A377073, A378180.
%K A378183 nonn,easy
%O A378183 1,4
%A A378183 _Michael De Vlieger_, Nov 19 2024