%I #10 Mar 23 2023 07:35:15
%S 0,4,6,8,10,34,14,16,15,54,22,74,26,74,76,32,34,97,38,118,104,114,46,
%T 154,35,134,42,162,58,324,62,64,160,174,164,209,74,194,188,246,82,440,
%U 86,250,220,234,94,314,63,229,244,294,106,286,252,338,272,294,118,724,122,314
%N a(n) = Sum_{p|n, p prime} Sum_{d|n} lcm(d,p).
%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>
%F a(p) = 2*p, p prime.
%e a(6) = 34; a(6) = Sum_{p|6, p prime} Sum_{d|6} lcm(d,p) = Sum_{p|6, p prime} (lcm(1,p) + lcm(2,p) + lcm(3,p) + lcm(6,p)) = (lcm(1,2) + lcm(2,2) + lcm(3,2) + lcm(6,2)) + (lcm(1,3) + lcm(2,3) + lcm(3,3) + lcm(6,3)) = (2+2+6+6) + (3+6+3+6) = 34.
%o (PARI) a(n) = my(f=factor(n), d=divisors(f)); sum(k=1, #f~, sum(j=1, #d, lcm(d[j], f[k,1]))); \\ _Michel Marcus_, Feb 19 2022
%Y Cf. A351711.
%K nonn
%O 1,2
%A _Wesley Ivan Hurt_, Feb 18 2022