A352167 - OEIS

A352167

a(n) is the sum of the prime factors of n (with multiplicity) that are less than n.

0, 0, 0, 4, 0, 5, 0, 6, 6, 7, 0, 7, 0, 9, 8, 8, 0, 8, 0, 9, 10, 13, 0, 9, 10, 15, 9, 11, 0, 10, 0, 10, 14, 19, 12, 10, 0, 21, 16, 11, 0, 12, 0, 15, 11, 25, 0, 11, 14, 12, 20, 17, 0, 11, 16, 13, 22, 31, 0, 12, 0, 33, 13, 12, 18, 16, 0, 21, 26, 14, 0, 12, 0, 39, 13, 23, 18, 18, 0, 13

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OFFSET

1,4

LINKS

Table of n, a(n) for n=1..80.

Eric Weisstein's World of Mathematics, Sum of Prime Factors

FORMULA

a(n) = 0 if n is prime, A001414(n) otherwise.

a(n) = A001414(n) - A061397(n).

MATHEMATICA

a[n_] := If[n == 1 || PrimeQ[n], 0, Plus @@ Times @@@ FactorInteger@n]; Table[a[n], {n, 80}]

PROG