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

1,2

Links

Table of n, a(n) for n=1..75.

Formula

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A222416 A269524 A161656 * A225090 A162683 A073137

Adjacent sequences: A306325 A306326 A306327 * A306329 A306330 A306331

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 07 2019

Status

approved