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%I #9 Sep 08 2022 08:46:25
%S 1,7,5,28,7,23,9,88,44,49,13,128,15,39,35,243,19,140,21,112,45,55,25,
%T 308,100,105,84,228,31,161,33,369,65,133,63,1064,39,87,75,532,43,183,
%U 45,160,152,103,49,1083,66,328,95,420,55,300,91,408,105,217,61,476
%N a(n) = Sum_{d|n} lcm(tau(d), sigma(d)).
%F a(p) = p + 2 for p = odd primes (A065091).
%e a(6) = lcm(tau(1), sigma(1)) + lcm(tau(2), sigma(2)) + lcm(tau(3), sigma(3)) + lcm(tau(6), sigma(6)) = lcm(1, 1) + lcm(2, 3) + lcm(2, 4) + lcm(4, 12) = 1 + 6 + 4 + 12 = 23.
%t a[n_] := DivisorSum[n, LCM[DivisorSigma[0, #], DivisorSigma[1, #]] &]; Array[a, 100] (* _Amiram Eldar_, May 10 2020 *)
%o (Magma) [&+[LCM(#Divisors(d), &+Divisors(d)): d in Divisors(n)]: n in [1..100]]
%o (PARI) a(n) = sumdiv(n, d, lcm(numdiv(d), sigma(d))); \\ _Michel Marcus_, May 10 2020
%Y Cf. A334579 (Sum_{d|n} gcd(tau(d), sigma(d))), A334783 (Sum_{d|n} lcm(d, sigma(d))).
%Y Cf. A000005 (tau(n)), A000203 (sigma(n)), A009278 (lcm(tau(n), sigma(n))).
%K nonn
%O 1,2
%A _Jaroslav Krizek_, May 10 2020
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