A322177 If n = Product (p_j^k_j) then a(n) = Sum (prime(p_j)^prime(k_j)).

0, 9, 25, 27, 121, 34, 289, 243, 125, 130, 961, 52, 1681, 298, 146, 2187, 3481, 134, 4489, 148, 314, 970, 6889, 268, 1331, 1690, 3125, 316, 11881, 155, 16129, 177147, 986, 3490, 410, 152, 24649, 4498, 1706, 364, 32041, 323, 36481, 988, 246, 6898, 44521, 2212, 4913, 1340

Offset

1,2

Links

Table of n, a(n) for n=1..50.

Example

a(12) = a(2^2 * 3^1) = prime(2)^prime(2) + prime(3)^prime(1) = 3^3 + 5^2 = 52.

Mathematica

a[n_] := Plus @@ (Prime[#[[1]]]^Prime[#[[2]]] & /@ FactorInteger[n]); a[1] = 0; Table[a[n], {n, 50}]

Prog

(PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k, 1] = prime(f[k, 1])^prime(f[k, 2]); ); vecsum(f[, 1]); \\ Michel Marcus, Nov 30 2018

Crossrefs

Cf. A000040, A008475, A222416, A304251, A321874.

Sequence in context: A352492 A068583 A074852 * A346068 A352519 A321874

Adjacent sequences: A322174 A322175 A322176 * A322178 A322179 A322180

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 30 2018

Status

approved