A384812 If n = Product prime(i)^e(i) then a(n) = Sum prime(e(i)).

0, 2, 2, 3, 2, 4, 2, 5, 3, 4, 2, 5, 2, 4, 4, 7, 2, 5, 2, 5, 4, 4, 2, 7, 3, 4, 5, 5, 2, 6, 2, 11, 4, 4, 4, 6, 2, 4, 4, 7, 2, 6, 2, 5, 5, 4, 2, 9, 3, 5, 4, 5, 2, 7, 4, 7, 4, 4, 2, 7, 2, 4, 5, 13, 4, 6, 2, 5, 4, 6, 2, 8, 2, 4, 5, 5, 4, 6, 2, 9, 7, 4, 2, 7, 4, 4, 4, 7, 2, 7

Offset: 1

Author

Ilya Gutkovskiy, Jun 10 2025

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from exponents in factorization of n.
• Index entries for sequences computed from indices in prime factorization.

Crossrefs

Cf. A001222, A001414, A008472, A066328, A181819, A366988.

Programs

Maple

f:= proc(n) local t;
  add(ithprime(t[2]),t=ifactors(n)[2])
end proc:
map(f, [$1..100]); # Robert Israel, Jul 25 2025

Mathematica

Table[Plus @@ (Prime[#[[2]]] & /@ FactorInteger[n]), {n, 1, 90}]

PARI

a(n) = my(f=factor(n)); sum(k=1, #f~, prime(f[k,2])); \\ Michel Marcus, Jun 10 2025