%I #7 Feb 21 2019 04:16:46
%S 0,2,3,4,5,5,7,8,9,7,11,25,13,9,8,16,17,25,19,49,10,13,23,125,25,15,
%T 27,81,29,10,31,32,14,19,12,625,37,21,16,343,41,12,43,169,64,25,47,
%U 625,49,49,20,225,53,125,16,729,22,31,59,100,61,33,100,64,18,16,67,361,26,14,71,15625,73,39,64
%N If n = Product (p_j^k_j) then a(n) = Sum (p_j)^Product (k_j).
%F a(n) = sopf(n)^tau(n/rad(n)) = A008472(n)^A005361(n).
%e a(12) = a(2^2 * 3^1) = (2 + 3)^(2 * 1) = 25.
%t Table[DivisorSum[n, # &, PrimeQ[#] &]^DivisorSigma[0, n/Last[Select[Divisors[n], SquareFreeQ]]], {n, 75}]
%Y Cf. A005361, A008472, A088865, A246655 (fixed points), A285769, A303277, A303278, A306329.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Feb 07 2019