A304251 If n = Product (p_j^k_j) then a(n) = Sum (prime(p_j)^k_j).

0, 3, 5, 9, 11, 8, 17, 27, 25, 14, 31, 14, 41, 20, 16, 81, 59, 28, 67, 20, 22, 34, 83, 32, 121, 44, 125, 26, 109, 19, 127, 243, 36, 62, 28, 34, 157, 70, 46, 38, 179, 25, 191, 40, 36, 86, 211, 86, 289, 124, 64, 50, 241, 128, 42, 44, 72, 112, 277, 25, 283, 130, 42, 729, 52, 39, 331, 68, 88, 31

Offset: 1

Author

Ilya Gutkovskiy, May 09 2018

Keywords

• nonn

Examples

			a(12) = 14 because 12 = 2^2*3 and prime(2)^2 + prime(3) = 3^2 + 5 = 14.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Ilya Gutkovskiy, Scatter plot of a(n) up to n=100000
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000040, A002110, A006450, A008475, A038580, A064988, A083186, A222416, A304037, A304253 (fixed points).

Programs

Maple

f:= proc(n) local t;
   add(ithprime(t[1])^t[2],t=ifactors(n)[2])
end proc:
map(f, [$1..100]); # Robert Israel, Apr 25 2024

Mathematica

a[n_] := Plus @@ (Prime[#[[1]]]^#[[2]] & /@ FactorInteger[n]); a[1] = 0; Table[a[n], {n, 70}]

PARI

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

Formula

a(prime(i)^k) = prime(prime(i))^k.

a(A000040(k)) = A006450(k).

a(A006450(k)) = A038580(k).

a(A002110(k)) = A083186(k).