A303278 -id:A303278 - cp's OEIS frontend

A306328 If n = Product (p_j^k_j) then a(n) = Sum (p_j)^Product (k_j).

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, 27, 81, 29, 10, 31, 32, 14, 19, 12, 625, 37, 21, 16, 343, 41, 12, 43, 169, 64, 25, 47, 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

Offset: 1

Ilya Gutkovskiy, Feb 07 2019

nonn

			a(12) = a(2^2 * 3^1) = (2 + 3)^(2 * 1) = 25.

Cf. A005361, A008472, A088865, A246655 (fixed points), A285769, A303277, A303278, A306329.

Table[DivisorSum[n, # &, PrimeQ[#] &]^DivisorSigma[0, n/Last[Select[Divisors[n], SquareFreeQ]]], {n, 75}]

a(n) = sopf(n)^tau(n/rad(n)) = A008472(n)^A005361(n).

A306329 If n = Product (p_j^k_j) then a(n) = Product (p_j)^Sum (k_j).

Original entry on oeis.org

1, 2, 3, 4, 5, 36, 7, 8, 9, 100, 11, 216, 13, 196, 225, 16, 17, 216, 19, 1000, 441, 484, 23, 1296, 25, 676, 27, 2744, 29, 27000, 31, 32, 1089, 1156, 1225, 1296, 37, 1444, 1521, 10000, 41, 74088, 43, 10648, 3375, 2116, 47, 7776, 49, 1000, 2601, 17576, 53, 1296, 3025, 38416, 3249, 3364, 59, 810000

Offset: 1

Ilya Gutkovskiy, Feb 07 2019

nonn

			a(12) = a(2^2 * 3^1) = (2 * 3)^(2 + 1) = 216.

Cf. A000961 (fixed points), A001222, A007947, A088865, A285769, A303277, A303278, A306328.

Table[Last[Select[Divisors[n], SquareFreeQ]]^PrimeOmega[n], {n, 60}]

a(n) = rad(n)^bigomega(n) = A007947(n)^A001222(n).

cp's OEIS Frontend

A306328 If n = Product (p_j^k_j) then a(n) = Sum (p_j)^Product (k_j).

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