login
A345302
a(n) = Sum_{p|n, p prime} lcm(p,n/p).
5
0, 2, 3, 2, 5, 12, 7, 4, 3, 20, 11, 18, 13, 28, 30, 8, 17, 24, 19, 30, 42, 44, 23, 36, 5, 52, 9, 42, 29, 90, 31, 16, 66, 68, 70, 30, 37, 76, 78, 60, 41, 126, 43, 66, 60, 92, 47, 72, 7, 60, 102, 78, 53, 72, 110, 84, 114, 116, 59, 150, 61, 124, 84, 32, 130, 198, 67, 102, 138, 210
OFFSET
1,2
COMMENTS
If p is prime, a(p) = Sum_{p|p} lcm(p,p/p) = p.
EXAMPLE
a(12) = Sum_{p|12} lcm(p,12/p) = lcm(2,6) + lcm(3,4) = 6 + 12 = 18.
MATHEMATICA
Table[Sum[LCM[k, n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 13 2021
STATUS
approved