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A306956
Sum over all partitions of n into distinct parts of the LCM of the parts.
3
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
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 *)
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 17 2019
STATUS
approved