This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A327781 #17 May 18 2021 08:41:28
%S A327781 0,0,1,2,4,5,9,12,18,22,30,37,52,69,89,110,143,163,204,243,298,374,
%T A327781 451,516,620,790,932,1064,1243,1454,1699,2365,2733,3071,3524,3945,
%U A327781 4526,5600,6361,7111,8057,9405,10621,12836,14395,16066,18047,19860,22143,25748
%N A327781 Number of integer partitions of n whose LCM is less than n.
%H A327781 Alois P. Heinz, <a href="/A327781/b327781.txt">Table of n, a(n) for n = 0..500</a>
%e A327781 The a(2) = 1 through a(8) = 18 partitions:
%e A327781 (11) (21) (22) (41) (33) (61) (44)
%e A327781 (111) (31) (221) (42) (322) (62)
%e A327781 (211) (311) (51) (331) (71)
%e A327781 (1111) (2111) (222) (421) (332)
%e A327781 (11111) (411) (511) (422)
%e A327781 (2211) (2221) (611)
%e A327781 (3111) (3211) (2222)
%e A327781 (21111) (4111) (3221)
%e A327781 (111111) (22111) (3311)
%e A327781 (31111) (4211)
%e A327781 (211111) (5111)
%e A327781 (1111111) (22211)
%e A327781 (32111)
%e A327781 (41111)
%e A327781 (221111)
%e A327781 (311111)
%e A327781 (2111111)
%e A327781 (11111111)
%p A327781 a:= proc(m) option remember; local b; b:=
%p A327781 proc(n, i, l) option remember; `if`(n=0, 1,
%p A327781 `if`(i>1, b(n, i-1, l), 0) +(h-> `if`(h<m,
%p A327781 b(n-i, min(n-i, i), h), 0))(ilcm(l, i)))
%p A327781 end: `if`(m>0, b(m$2, 1), 0)
%p A327781 end:
%p A327781 seq(a(n), n=0..70); # _Alois P. Heinz_, Oct 10 2019
%t A327781 Table[Length[Select[IntegerPartitions[n],LCM@@#<n&]],{n,30}]
%t A327781 (* Second program: *)
%t A327781 a[m_] := a[m] = Module[{b}, b[n_, i_, l_] := b[n, i, l] =
%t A327781 If[n == 0, 1, If[i>1, b[n, i - 1, l], 0] + Function[h, If[h<m,
%t A327781 b[n - i, Min[n - i, i], h], 0]][LCM[l, i]]]; If[m>0, b[m, m, 1], 0]];
%t A327781 a /@ Range[0, 70] (* _Jean-François Alcover_, May 18 2021, after _Alois P. Heinz_ *)
%o A327781 (PARI)
%o A327781 b(m,n)={my(d=divisors(m)); polcoef(1/prod(i=1, #d, 1 - x^d[i] + O(x*x^n)), n)}
%o A327781 a(n)={sum(m=1, n-1, b(m, n)*sum(i=1, (n-1)\m, moebius(i)))} \\ _Andrew Howroyd_, Oct 09 2019
%Y A327781 The Heinz numbers of these partitions are given by A327776.
%Y A327781 Partitions whose LCM is equal to their sum are A074761.
%Y A327781 Partitions whose LCM is greater than their sum are A327779.
%Y A327781 Cf. A018818, A290103, A316413, A319333, A326842, A327778, A327780.
%K A327781 nonn
%O A327781 0,4
%A A327781 _Gus Wiseman_, Sep 25 2019