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%I #16 Sep 08 2022 08:46:25
%S 1,7,13,35,31,31,57,155,130,127,133,143,183,231,163,651,307,382,381,
%T 575,741,535,553,383,806,735,1210,315,871,631,993,2667,673,1231,1767,
%U 3770,1407,1527,2379,1055,1723,1599,1893,1487,1450,2215,2257,2367,2850,5552
%N a(n) = Sum_{d|n} lcm(d, sigma(d)).
%H Robert Israel, <a href="/A334783/b334783.txt">Table of n, a(n) for n = 1..10000</a>
%H Robert Israel, <a href="/A334783/a334783.png">Plot of a(n)/n^2 for n=1..20000</a>
%F a(p) = p^2 + p + 1 for p = primes (A000040).
%e a(6) = lcm(1, sigma(1)) + lcm(2, sigma(2)) + lcm(3, sigma(3)) + lcm(6, sigma(6)) = lcm(1, 1) + lcm(2, 3) + lcm(3, 4) + lcm(6, 12) = 1 + 6 + 12 + 12 = 31.
%p N:= 100: # for a(1)..a(N)
%p V:= Vector(N):
%p for d from 1 to N do
%p t:= ilcm(d,numtheory:-sigma(d));
%p R:= [seq(i,i=d..N,d)];
%p V[R]:= V[R] +~ t;
%p od:
%p convert(V,list); # _Robert Israel_, May 13 2020
%t a[n_] := DivisorSum[n, LCM[#, DivisorSigma[1, #]] &]; Array[a, 100] (* _Amiram Eldar_, May 10 2020 *)
%o (Magma) [&+[LCM(d, &+Divisors(d)): d in Divisors(n)]: n in [1..100]]
%o (PARI) a(n) = sumdiv(n, d, lcm(d, sigma(d))); \\ _Michel Marcus_, May 10 2020
%Y Cf. A334490 (Sum_{d|n} gcd(d, sigma(d))), A334782 (Sum_{d|n} lcm(d, tau(d))).
%Y Cf. A000005 (tau(n)), A000203 (sigma(n)), A009242 (lcm(n, sigma(n))).
%K nonn,look
%O 1,2
%A _Jaroslav Krizek_, May 10 2020
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