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 A371171 #7 Mar 16 2024 21:41:09
%S A371171 0,0,1,1,2,4,5,9,12,18,26,34,50,65,92,121,161,209,274,353,456,590,745,
%T A371171 950,1195,1507,1885,2350,2923,3611,4465,5485,6735,8223,10050,12195,
%U A371171 14822,17909,21653,26047,31340,37557,44990,53708,64068,76241,90583,107418
%N A371171 Number of integer partitions of n with more parts than distinct divisors of parts.
%C A371171 The Heinz numbers of these partitions are given by A370348.
%e A371171 The partition (3,2,1,1) has 4 parts {1,2,3,4} and 3 distinct divisors of parts {1,2,3}, so is counted under a(7).
%e A371171 The a(0) = 0 through a(8) = 12 partitions:
%e A371171 . . (11) (111) (211) (221) (222) (331) (2222)
%e A371171 (1111) (311) (2211) (511) (3221)
%e A371171 (2111) (3111) (2221) (3311)
%e A371171 (11111) (21111) (3211) (4211)
%e A371171 (111111) (4111) (5111)
%e A371171 (22111) (22211)
%e A371171 (31111) (32111)
%e A371171 (211111) (41111)
%e A371171 (1111111) (221111)
%e A371171 (311111)
%e A371171 (2111111)
%e A371171 (11111111)
%t A371171 Table[Length[Select[IntegerPartitions[n],Length[#] > Length[Union@@Divisors/@#]&]],{n,0,30}]
%Y A371171 The partitions are ranked by A370348.
%Y A371171 The opposite version is A371173, ranked by A371168.
%Y A371171 The RHS is represented by A370820, positions of twos A371127.
%Y A371171 The version for equality is A371130 (ranks A370802), strict A371128.
%Y A371171 For submultisets instead of parts on the LHS we get ranks A371167.
%Y A371171 A000005 counts divisors.
%Y A371171 Choosable partitions: A239312 (A368110), A355740 (A370320), A370592 (A368100), A370593 (A355529).
%Y A371171 Cf. A003963, A319055, A355731, A370803, A370808, A370809, A370813, A370814.
%K A371171 nonn
%O A371171 1,5
%A A371171 _Gus Wiseman_, Mar 16 2024