A345306 - OEIS

A345306

a(n) = n * Sum_{p|n, p prime} lcm(p,n/p) / p.

0, 2, 3, 4, 5, 30, 7, 16, 9, 70, 11, 84, 13, 126, 120, 64, 17, 198, 19, 180, 210, 286, 23, 336, 25, 390, 81, 308, 29, 930, 31, 256, 462, 646, 420, 468, 37, 798, 624, 720, 41, 1722, 43, 660, 630, 1150, 47, 1344, 49, 1350, 1020, 884, 53, 1782, 880, 1232, 1254, 1798, 59

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OFFSET

1,2

COMMENTS

If p is prime, a(p) = p * Sum_{p|p} lcm(p,p/p) / p = p * p/p = p.

LINKS

Table of n, a(n) for n=1..59.

Index entries for sequences related to lcm's

EXAMPLE

a(18) = 18 * Sum_{p|18} lcm(p,18/p) / p = 18 * (lcm(2,9)/2 + lcm(3,6)/3) = 18 * (9 + 2) = 198.

MATHEMATICA

Table[n*Sum[(1/k) LCM[k, n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]