A378314 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).

0, 1, 2, 4, 6, 12, 16, 28, 36, 52, 70, 118, 150, 246, 318, 382, 430, 670, 798, 1278, 1566, 1886, 2270, 3230, 3742, 4702, 5854, 6814, 7966, 11806, 14878, 22558, 25630, 32542, 40222, 46366, 52510, 70942, 86302, 100126, 112414, 149278, 172318, 246046, 295198, 344350, 405790, 553246, 626974, 774430, 897310

Offset

0,3

Links

Table of n, a(n) for n=0..50.

Formula

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

Example

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

Prog

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

Crossrefs

Partial sums of A190940.

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

Sequence in context: A293132 A098895 A266543 * A330711 A220219 A284456

Adjacent sequences: A378311 A378312 A378313 * A378316 A378317 A378318

Keyword

nonn

Author

Max Alekseyev, Nov 22 2024

Status

approved