Let s = {1,2,…,n}. Then a(n) = total(d(s))^2 - total(d(s)^3), where d(s) is the number of divisors.
0, 0, 8, 20, 48, 80, 132, 212, 314, 450, 554, 722, 858, 1106, 1386, 1736, 1932, 2376, 2604, 3144, 3624, 4136, 4428, 5196, 5682, 6330, 7010, 7970, 8370, 9570, 10010, 11186, 12090, 13026, 13994, 15704, 16260, 17348, 18468, 20420, 21048, 23160, 23828, 25688
1
Because s is an n-tuple, d(s) is an n-tuple giving the number of divisors of every number in s.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
(Mma) Table[s = Range[n]; Total[DivisorSigma[0, s]]^2 - Total[DivisorSigma[0, s]^3], {n, 50}]
Cf. A000005 (sum of divisors of n), S000462, S000463, S000464.
nonn
T. D. Noe, Feb 02 2015