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

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Wikipedia, Partition (number theory)

Formula

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

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

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

Maple

b:= proc(n, i, r) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0,
       r, b(n, i-1, r) +b(n-i, min(i-1, n-i), ilcm(i, r))))
    end:
a:= n-> 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 *)

Crossrefs

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

Sequence in context: A245921 A215513 A358878 * A337655 A366175 A111328

Adjacent sequences: A306953 A306954 A306955 * A306957 A306958 A306959

Keyword

nonn

Author

Alois P. Heinz, Mar 17 2019

Status

approved