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A304251
If n = Product (p_j^k_j) then a(n) = Sum (prime(p_j)^k_j).
3
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
1,2
FORMULA
a(prime(i)^k) = prime(prime(i))^k.
a(A000040(k)) = A006450(k).
a(A006450(k)) = A038580(k).
a(A002110(k)) = A083186(k).
EXAMPLE
a(12) = 14 because 12 = 2^2*3 and prime(2)^2 + prime(3) = 3^2 + 5 = 14.
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}]
PROG
(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, prime(f[k, 1])^f[k, 2]); \\ Michel Marcus, May 09 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 09 2018
STATUS
approved