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 A328221 #4 Oct 16 2019 08:45:35
%S A328221 0,0,1,2,4,5,10,12,20,26,38,51,73,92,126,166,219,283,369,470,604,763,
%T A328221 968,1217,1534,1907,2376,2944,3640,4476,5501,6723,8212,9986,12130,
%U A328221 14682,17748,21376,25717,30847,36959,44152,52688,62714,74557,88440,104775,123878
%N A328221 Number of integer partitions of n with at least one pair of consecutive divisible parts.
%C A328221 Includes all non-strict partitions.
%e A328221 The a(2) = 1 through a(8) = 20 partitions:
%e A328221 (11) (21) (22) (41) (33) (61) (44)
%e A328221 (111) (31) (221) (42) (322) (62)
%e A328221 (211) (311) (51) (331) (71)
%e A328221 (1111) (2111) (222) (421) (332)
%e A328221 (11111) (321) (511) (422)
%e A328221 (411) (2221) (431)
%e A328221 (2211) (3211) (521)
%e A328221 (3111) (4111) (611)
%e A328221 (21111) (22111) (2222)
%e A328221 (111111) (31111) (3221)
%e A328221 (211111) (3311)
%e A328221 (1111111) (4211)
%e A328221 (5111)
%e A328221 (22211)
%e A328221 (32111)
%e A328221 (41111)
%e A328221 (221111)
%e A328221 (311111)
%e A328221 (2111111)
%e A328221 (11111111)
%t A328221 Table[Length[Select[IntegerPartitions[n],MatchQ[#,{___,x_,y_,___}/;Divisible[x,y]]&]],{n,0,30}]
%Y A328221 The complement is counted by A328171.
%Y A328221 Partitions whose consecutive parts are relatively prime are A328172.
%Y A328221 Partitions with no pair of consecutive parts relatively prime are A328187.
%Y A328221 Numbers without consecutive divisible proper divisors are A328028.
%Y A328221 Cf. A000837, A018783, A328026, A328161, A328188, A328189, A328194, A328220.
%K A328221 nonn
%O A328221 0,4
%A A328221 _Gus Wiseman_, Oct 15 2019