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%I #10 Sep 08 2022 08:46:25
%S 1,3,7,15,11,21,15,23,16,33,23,45,27,45,77,103,35,48,39,105,105,69,47,
%T 77,86,81,124,141,59,231,63,199,161,105,165,108,75,117,189,153,83,315,
%U 87,213,176,141,95,397,162,258,245,249,107,372,253,205,273,177
%N a(n) = Sum_{d|n} lcm(d, tau(d)).
%F a(p) = 2p + 1 for p = odd primes (A065091).
%e a(6) = lcm(1, tau(1)) + lcm(2, tau(2)) + lcm(3, tau(3)) + lcm(6, tau(6)) = lcm(1, 1) + lcm(2, 2) + lcm(3, 2) + lcm(6, 4) = 1 + 2 + 6 + 12 = 21.
%t a[n_] := DivisorSum[n, LCM[#, DivisorSigma[0, #]] &]; 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, numdiv(d))); \\ _Michel Marcus_, May 10 2020
%Y Cf. A322979 (Sum_{d|n} gcd(d, tau(d))), A334783 (Sum_{d|n} lcm(d, sigma(d))).
%Y Cf. A000005 (tau(n)), A000203 (sigma(n)), A009230 (lcm(n, tau(n))).
%K nonn
%O 1,2
%A _Jaroslav Krizek_, May 10 2020