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 A371284 #5 Mar 22 2024 09:16:47
%S A371284 0,1,1,2,3,4,5,8,9,11,12,16,18,23,25,32,36,42,47,57,62,73,81,96,106,
%T A371284 123,132,154,168,190,207,240,259,293,317,359,388,434,469,529,574,635,
%U A371284 688,768,826,915,987,1093,1181,1302,1397,1540,1662,1818,1959,2149,2309
%N A371284 Number of integer partitions of n whose distinct parts form the set of divisors of some number.
%C A371284 The Heinz numbers of these partitions are given by A371288.
%e A371284 The partition y = (10,5,5,5,2,2,1) has distinct parts {1,2,5,10}, which form the set of divisors of 10, so y is counted under a(30).
%e A371284 The a(1) = 1 through a(8) = 9 partitions:
%e A371284 (1) (11) (21) (31) (221) (51) (331) (71)
%e A371284 (111) (211) (311) (2211) (421) (3311)
%e A371284 (1111) (2111) (3111) (511) (4211)
%e A371284 (11111) (21111) (2221) (5111)
%e A371284 (111111) (22111) (22211)
%e A371284 (31111) (221111)
%e A371284 (211111) (311111)
%e A371284 (1111111) (2111111)
%e A371284 (11111111)
%t A371284 Table[Length[Select[IntegerPartitions[n], Union[#]==Divisors[Max[#]]&]],{n,0,30}]
%Y A371284 The strict case is A054973, ranks A371283 (unsorted version A275700).
%Y A371284 These partitions have ranks A371288.
%Y A371284 A000005 counts divisors, row-lengths of A027750.
%Y A371284 A000041 counts integer partitions, strict A000009.
%Y A371284 A008284 counts partitions by length, strict A008289.
%Y A371284 Cf. A001221, A002865, A239312, A370803, A371172, A371286, A371285.
%K A371284 nonn
%O A371284 0,4
%A A371284 _Gus Wiseman_, Mar 22 2024