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 A371128 #6 Mar 19 2024 08:38:12
%S A371128 1,1,0,1,1,0,2,1,2,1,2,2,3,3,3,5,3,5,6,7,7,8,8,9,12,13,13,14,15,16,19,
%T A371128 23,25,26,26,27,36,37,40,42,46,50,55,66,65,71,71,82,90,102,103,114,
%U A371128 117,130,147,154,166,176,182,194,228,239,259,267,287,307,336
%N A371128 Number of strict integer partitions of n containing all distinct divisors of all parts.
%C A371128 Also strict integer partitions such that the number of parts is equal to the number of distinct divisors of all parts.
%e A371128 The a(9) = 1 through a(19) = 7 partitions (A..H = 10..17):
%e A371128 531 721 731 B1 751 D1 B31 D21 B51 H1 B71
%e A371128 4321 5321 5421 931 B21 7521 7531 D31 9531 D51
%e A371128 6321 7321 7421 8421 64321 B321 A521 B521
%e A371128 9321 65321 B421 D321
%e A371128 54321 74321 75321 75421
%e A371128 84321 76321
%e A371128 94321
%t A371128 Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&SubsetQ[#,Union@@Divisors/@#]&]],{n,0,30}]
%Y A371128 The LHS is represented by A001221, distinct case of A001222.
%Y A371128 The RHS is represented by A370820, for prime factors A303975.
%Y A371128 Strict case of A371130 (ranks A370802) and A371178 (ranks A371177).
%Y A371128 The complement is counted by A371180, non-strict A371132.
%Y A371128 A000005 counts divisors.
%Y A371128 A000041 counts integer partitions, strict A000009.
%Y A371128 A008284 counts partitions by length.
%Y A371128 A305148 counts partitions without divisors, strict A303362, ranks A316476.
%Y A371128 Cf. A000837, A003963, A239312, A285573, A319055, A370803, A370808, A371171, A371172, A371173.
%K A371128 nonn
%O A371128 0,7
%A A371128 _Gus Wiseman_, Mar 18 2024