A306956 Sum over all partitions of n into distinct parts of the LCM of the parts.

1, 1, 2, 5, 7, 15, 21, 39, 58, 90, 142, 218, 325, 465, 695, 948, 1411, 1977, 2883, 3940, 5415, 7422, 10126, 14091, 18947, 25666, 34282, 45890, 60710, 82211, 108510, 142960, 185271, 240595, 315158, 409231, 531967, 688689, 880997, 1126451, 1447754, 1849743

Offset: 0

Author

Alois P. Heinz, Mar 17 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200
• Wikipedia, Partition (number theory)

Crossrefs

Cf. A000009, A000041, A001560, A040051, A052002, A181844, A319301.

Programs

Maple

b:= proc(n, i, r) option remember; `if`(i*(i+1)/2 b(n$2, 1):
seq(a(n), n=0..44);

Mathematica

b[n_, i_, r_] := b[n, i, r] = If[i(i+1)/2 < n, 0, If[n == 0, r, b[n, i-1, r] + b[n-i, Min[i-1, n-i], LCM[i, r]]]];
a[n_] := b[n, n, 1];
Table[a[n], {n, 0, 44}] (* Jean-François Alcover, Mar 20 2019, translated from Maple *)

Formula

a(n) mod 2 = A040051(n).

a(n) is even <=> n in { A001560 }.

a(n) is odd <=> n in { A052002 }.