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 A343380 #6 Apr 16 2021 15:46:04 %S A343380 1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,0,1,0,1,1,4,0,1,0,2,0,4,0,3,1,2, %T A343380 2,5,0,5,3,4,1,9,1,5,2,4,5,11,1,6,4,11,3,13,5,10,4,11,8,14,3,10,6,9,3, %U A343380 15,6,14,10,18,8 %N A343380 Number of strict integer partitions of n with no part dividing all the others but with a part divisible by all the others. %C A343380 Alternative name: Number of strict integer partitions of n that are either empty or (1) have smallest part not dividing all the others and (2) have greatest part divisible by all the others. %e A343380 The a(11) = 1 through a(29) = 4 partitions (empty columns indicated by dots, A..O = 10..24): %e A343380 632 . . . . . A52 . C43 . C432 C64 E72 . C643 . K52 . I92 %e A343380 C32 F53 C6432 K54 %e A343380 I32 O32 %e A343380 C632 I632 %t A343380 Table[Length[Select[IntegerPartitions[n],#=={}||UnsameQ@@#&&!And@@IntegerQ/@(#/Min@@#)&&And@@IntegerQ/@(Max@@#/#)&]],{n,0,30}] %Y A343380 The first condition alone gives A341450. %Y A343380 The non-strict version is A343344 (Heinz numbers: A343339). %Y A343380 The second condition alone gives A343347. %Y A343380 The half-opposite versions are A343378 and A343379. %Y A343380 The opposite (and dual) version is A343381. %Y A343380 A000009 counts strict partitions. %Y A343380 A000041 counts partitions. %Y A343380 A000070 counts partitions with a selected part. %Y A343380 A006128 counts partitions with a selected position. %Y A343380 A015723 counts strict partitions with a selected part. %Y A343380 A018818 counts partitions into divisors (strict: A033630). %Y A343380 A167865 counts strict chains of divisors > 1 summing to n. %Y A343380 A339564 counts factorizations with a selected factor. %Y A343380 Cf. A083710, A097986, A130689, A200745, A264401, A338470, A339562, A342193, A343377, A343382. %K A343380 nonn %O A343380 0,18 %A A343380 _Gus Wiseman_, Apr 16 2021