OFFSET
1,3
FORMULA
a(n) = Sum_{k=1..floor(n/2)} sopf(k*(n-k)).
EXAMPLE
a(7) = 17; The partitions of 7 into two positive integer parts are (6,1), (5,2), and (4,3). The sum of the distinct prime factors of 6*1, 5*2, and 4*3 are 5, 7, and 5 respectively. The total is then 5 + 7 + 5 = 17.
MATHEMATICA
Table[Sum[Sum[k (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[i (n - i)/k] + Floor[i (n - i)/k]), {k, i (n - i)}], {i, Floor[n/2]}], {n, 80}]
PROG
(PARI) a(n) = sum(k=1, n\2, vecsum(factor(k*(n-k))[, 1])); \\ Michel Marcus, Oct 31 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 08 2021
STATUS
approved