A378314 - OEIS

%I #14 Nov 23 2024 09:37:31

%S 0,1,2,4,6,12,16,28,36,52,70,118,150,246,318,382,430,670,798,1278,

%T 1566,1886,2270,3230,3742,4702,5854,6814,7966,11806,14878,22558,25630,

%U 32542,40222,46366,52510,70942,86302,100126,112414,149278,172318,246046,295198,344350,405790,553246,626974,774430,897310

%N a(n) = number of subsets of {1, 2, ..., n} that represent the first k divisors of m for some positive integers m and 1 <= k <= A000005(m).

%F a(n) = Sum_{i=1..n} sigma(LCM(1,2,...,i)/i).

%e a(4) = 6 enumerates subsets {1}, {1,2}, {1,2,3}, {1,2,4}, {1,2,3,4}, {1,3}.

%o (PARI) a378314(n) = my(L=1); sum(i=1,n, L=lcm(L,i); sigma(L/i));

%Y Partial sums of A190940.

%Y Cf. A001248, A027750, A064510, A180851, A194269, A307137, A378313.

%K nonn

%O 0,3

%A _Max Alekseyev_, Nov 22 2024