|
%I #10 Jun 14 2018 04:04:22
%S 1,1,1,4,1,32,1,9,8,128,1,243,1,512,256,16,1,243,1,2187,1024,8192,1,
%T 1024,32,32768,27,19683,1,59049,1,25,16384,524288,4096,1024,1,2097152,
%U 65536,16384,1,531441,1,1594323,6561,33554432,1,3125,128,2187,1048576,14348907,1,1024,65536
%N If n = Product (p_j^k_j) then a(n) = (Sum (k_j))^(Sum (p_j)).
%H Antti Karttunen, <a href="/A303277/b303277.txt">Table of n, a(n) for n = 1..4096</a>
%F a(n) = bigomega(n)^sopf(n) = A001222(n)^A008472(n).
%F a(p^k) = k^p where p is a prime.
%F a(A000312(k)) = a(k)*k^A008472(k).
%F a(A000142(k)) = A022559(k)^A034387(k).
%F a(A002110(k)) = k^A007504(k).
%e a(48) = a(2^4 * 3^1) = (4 + 1)^(2 + 3) = 5^5 = 3125.
%t Join[{1}, Table[PrimeOmega[n]^DivisorSum[n, # &, PrimeQ[#] &], {n, 2, 55}]]
%o (PARI) a(n) = my(f=factor(n)); vecsum(f[,2])^vecsum(f[,1]); \\ _Michel Marcus_, Apr 21 2018
%Y Cf. A000142, A000312, A001222, A002110, A007504, A008472, A008474, A008477, A022559, A034387, A039697, A088865, A263653, A285769.
%K nonn
%O 1,4
%A _Ilya Gutkovskiy_, Apr 20 2018
|
