A304251 -id:A304251 - cp's OEIS frontend

A304253 Numbers k such that k = Product (p_j^e_j) = Sum (prime(p_j)^e_j).

20, 68, 76, 92, 8248

Offset: 1

Ilya Gutkovskiy, May 09 2018

Fixed points of A304251.

			68 is a term because 68 = 2^2*17 = prime(1)^2*prime(7) = prime(prime(1))^2 + prime(prime(7)).
8248 is a term because 8248 = 2^3*1031 = prime(1)^3*prime(173) = prime(prime(1))^3 + prime(prime(173)).

Index entries for sequences computed from indices in prime factorization

Cf. A006450, A008478, A048768, A304194, A304251.

a[n_] := Plus @@ (Prime[#[[1]]]^#[[2]] & /@ FactorInteger[n]); Select[Range[10000], a[#] == # &]

isok(n) = my(f=factor(n)); n == sum(k=1, #f~, prime(f[k,1])^f[k,2]); \\ Michel Marcus, May 09 2018

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

Original entry on oeis.org

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

Ilya Gutkovskiy, Nov 30 2018

nonn

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

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

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

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

cp's OEIS Frontend

A304253 Numbers k such that k = Product (p_j^e_j) = Sum (prime(p_j)^e_j).

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