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A328164
Number of integer partitions of n whose unsigned differences have the same GCD as the GCD of their parts all minus 1.
4
1, 1, 1, 2, 3, 6, 7, 13, 17, 25, 33, 51, 62, 92, 116, 160, 203, 281, 341, 469, 572, 754, 929, 1221, 1466, 1912, 2306, 2937, 3548, 4499, 5353, 6764, 8062, 10006, 11946, 14764, 17455, 21502, 25425, 30949, 36579, 44393, 52132, 63042, 74000, 88709, 104098, 124448
OFFSET
0,4
COMMENTS
Zeros are ignored when computing GCD, and the empty set has GCD 0.
EXAMPLE
The a(1) = 1 through a(8) = 17 partitions:
(1) (11) (21) (31) (32) (51) (43) (53)
(111) (211) (41) (321) (61) (71)
(1111) (221) (411) (322) (332)
(311) (2211) (331) (431)
(2111) (3111) (421) (521)
(11111) (21111) (511) (611)
(111111) (2221) (3221)
(3211) (3311)
(4111) (4211)
(22111) (5111)
(31111) (22211)
(211111) (32111)
(1111111) (41111)
(221111)
(311111)
(2111111)
(11111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], GCD@@Differences[#]==GCD@@(#-1)&]], {n, 0, 30}]
CROSSREFS
The complement to these partitions is counted by A328163.
The GCD of the divisors of n all minus 1 is A258409(n).
The GCD of the prime indices of n all minus 1 is A328167(n).
Partitions whose parts minus 1 are relatively prime are A328170.
Sequence in context: A304709 A330145 A183558 * A294916 A233423 A328024
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 07 2019
STATUS
approved