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

%I A306956 #17 Mar 20 2019 11:53:08
%S A306956 1,1,2,5,7,15,21,39,58,90,142,218,325,465,695,948,1411,1977,2883,3940,
%T A306956 5415,7422,10126,14091,18947,25666,34282,45890,60710,82211,108510,
%U A306956 142960,185271,240595,315158,409231,531967,688689,880997,1126451,1447754,1849743
%N A306956 Sum over all partitions of n into distinct parts of the LCM of the parts.
%H A306956 Alois P. Heinz, <a href="/A306956/b306956.txt">Table of n, a(n) for n = 0..200</a>
%H A306956 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_(number_theory)">Partition (number theory)</a>
%F A306956 a(n) mod 2 = A040051(n).
%F A306956 a(n) is even <=> n in { A001560 }.
%F A306956 a(n) is odd  <=> n in { A052002 }.
%p A306956 b:= proc(n, i, r) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0,
%p A306956        r, b(n, i-1, r) +b(n-i, min(i-1, n-i), ilcm(i, r))))
%p A306956     end:
%p A306956 a:= n-> b(n$2, 1):
%p A306956 seq(a(n), n=0..44);
%t A306956 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]]]];
%t A306956 a[n_] := b[n, n, 1];
%t A306956 Table[a[n], {n, 0, 44}] (* _Jean-François Alcover_, Mar 20 2019, translated from Maple *)
%Y A306956 Cf. A000009, A000041, A001560, A040051, A052002, A181844, A319301.
%K A306956 nonn
%O A306956 0,3
%A A306956 _Alois P. Heinz_, Mar 17 2019