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 A328164 #5 Oct 09 2019 10:02:54
%S A328164 1,1,1,2,3,6,7,13,17,25,33,51,62,92,116,160,203,281,341,469,572,754,
%T A328164 929,1221,1466,1912,2306,2937,3548,4499,5353,6764,8062,10006,11946,
%U A328164 14764,17455,21502,25425,30949,36579,44393,52132,63042,74000,88709,104098,124448
%N A328164 Number of integer partitions of n whose unsigned differences have the same GCD as the GCD of their parts all minus 1.
%C A328164 Zeros are ignored when computing GCD, and the empty set has GCD 0.
%e A328164 The a(1) = 1 through a(8) = 17 partitions:
%e A328164 (1) (11) (21) (31) (32) (51) (43) (53)
%e A328164 (111) (211) (41) (321) (61) (71)
%e A328164 (1111) (221) (411) (322) (332)
%e A328164 (311) (2211) (331) (431)
%e A328164 (2111) (3111) (421) (521)
%e A328164 (11111) (21111) (511) (611)
%e A328164 (111111) (2221) (3221)
%e A328164 (3211) (3311)
%e A328164 (4111) (4211)
%e A328164 (22111) (5111)
%e A328164 (31111) (22211)
%e A328164 (211111) (32111)
%e A328164 (1111111) (41111)
%e A328164 (221111)
%e A328164 (311111)
%e A328164 (2111111)
%e A328164 (11111111)
%t A328164 Table[Length[Select[IntegerPartitions[n],GCD@@Differences[#]==GCD@@(#-1)&]],{n,0,30}]
%Y A328164 The complement to these partitions is counted by A328163.
%Y A328164 The GCD of the divisors of n all minus 1 is A258409(n).
%Y A328164 The GCD of the prime indices of n all minus 1 is A328167(n).
%Y A328164 Partitions whose parts minus 1 are relatively prime are A328170.
%Y A328164 Cf. A000837, A018783, A175342, A279945, A289508, A328168, A328169.
%K A328164 nonn
%O A328164 0,4
%A A328164 _Gus Wiseman_, Oct 07 2019