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

Offset: 1

Author

Ilya Gutkovskiy, Mar 06 2022

Keywords

• nonn

Links

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

Crossrefs

Cf. A001414, A061397, A105221, A144494.

Programs

Mathematica

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

PARI

a(n) = if (isprime(n), 0, my(f=factor(n)); sum(k=1, #f~, f[k,1]*f[k,2])); \\ Michel Marcus, Mar 07 2022

Formula

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

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