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 A325765 #5 May 21 2019 22:05:27
%S A325765 1,1,1,2,1,3,1,3,2,3,1,5,1,3,3,4,1,5,1,5,3,3,1,7,2,3,3,5,1,7,1,5,3,3,
%T A325765 3,8,1,3,3,7,1,7,1,5,5,3,1,9,2,5,3
%N A325765 Number of integer partitions of n with a unique consecutive subsequence summing to every positive integer from 1 to n.
%C A325765 After a(0) = 1, same as A032741(n + 1) (number of proper divisors of n + 1).
%C A325765 The Heinz numbers of these partitions are given by A325764.
%e A325765 The a(1) = 1 through a(13) = 3 partitions:
%e A325765 (1) (11) (21) (1111) (221) (111111) (2221) (3311)
%e A325765 (111) (311) (4111) (11111111)
%e A325765 (11111) (1111111)
%e A325765 .
%e A325765 (22221) (1111111111) (33311) (111111111111) (2222221)
%e A325765 (51111) (44111) (7111111)
%e A325765 (111111111) (222221) (1111111111111)
%e A325765 (611111)
%e A325765 (11111111111)
%t A325765 normQ[m_]:=Or[m=={},Union[m]==Range[Max[m]]];
%t A325765 Table[Length[Select[IntegerPartitions[n],normQ[Total/@Union[ReplaceList[#,{___,s__,___}:>{s}]]]&&UnsameQ@@Total/@Union[ReplaceList[#,{___,s__,___}:>{s}]]&]],{n,0,20}]
%Y A325765 Cf. A000041, A002033, A103295, A103300, A143823, A169942, A325676, A325683, A325768, A325769, A325770.
%K A325765 nonn,more
%O A325765 0,4
%A A325765 _Gus Wiseman_, May 20 2019