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a(n) = Sum_{p|n, p prime} lcm(p,n/p).
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%I #12 Feb 05 2024 14:18:25

%S 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,

%T 9,42,29,90,31,16,66,68,70,30,37,76,78,60,41,126,43,66,60,92,47,72,7,

%U 60,102,78,53,72,110,84,114,116,59,150,61,124,84,32,130,198,67,102,138,210

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

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

%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>

%e a(12) = Sum_{p|12} lcm(p,12/p) = lcm(2,6) + lcm(3,4) = 6 + 12 = 18.

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

%Y Cf. A008472, A057670, A345266.

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Jun 13 2021