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 A342515 #8 Mar 22 2021 15:01:02
%S A342515 1,1,1,2,2,3,3,5,4,5,5,6,6,8,8,9,8,9,9,11,10,13,11,12,12,13,14,14,15,
%T A342515 15,16,18,16,17,17,19,18,20,20,22,21,21,23,23,22,24,23,24,24,27,25,26,
%U A342515 27,27,27,28,29,31,29,30,31,32,33,35,32,35,33,35,34,35
%N A342515 Number of strict partitions of n with constant (equal) first-quotients.
%C A342515 Also the number of reversed strict partitions of n with constant (equal) first-quotients.
%C A342515 The first quotients of a sequence are defined as if the sequence were an increasing divisor chain, so for example the quotients of (6,3,1) are (1/2,1/3).
%H A342515 Wikipedia, <a href="https://en.wikipedia.org/wiki/Arithmetic_progression">Arithmetic progression</a>
%H A342515 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%H A342515 Gus Wiseman, <a href="/A069916/a069916.txt">Sequences counting and ranking partitions and compositions by their differences and quotients.</a>
%e A342515 The a(1) = 1 through a(15) = 9 partitions (A..F = 10..15):
%e A342515 1 2 3 4 5 6 7 8 9 A B C D E F
%e A342515 21 31 32 42 43 53 54 64 65 75 76 86 87
%e A342515 41 51 52 62 63 73 74 84 85 95 96
%e A342515 61 71 72 82 83 93 94 A4 A5
%e A342515 421 81 91 92 A2 A3 B3 B4
%e A342515 A1 B1 B2 C2 C3
%e A342515 C1 D1 D2
%e A342515 931 842 E1
%e A342515 8421
%t A342515 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&SameQ@@Divide@@@Partition[#,2,1]&]],{n,0,30}]
%Y A342515 The version for differences instead of quotients is A049980.
%Y A342515 The non-strict ordered version is A342495.
%Y A342515 The non-strict version is A342496.
%Y A342515 The distinct instead of equal version is A342520.
%Y A342515 A000005 counts constant partitions.
%Y A342515 A000041 counts partitions (strict: A000009).
%Y A342515 A001055 counts factorizations (strict: A045778, ordered: A074206).
%Y A342515 A003238 counts chains of divisors summing to n - 1 (strict: A122651).
%Y A342515 A154402 counts partitions with adjacent parts x = 2y.
%Y A342515 A167865 counts strict chains of divisors > 1 summing to n.
%Y A342515 A175342 counts compositions with equal differences.
%Y A342515 Cf. A003242, A005117, A049988, A057567, A067824, A253249, A307824, A318991, A318992, A325328, A342086.
%K A342515 nonn
%O A342515 0,4
%A A342515 _Gus Wiseman_, Mar 19 2021