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A328164
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Number of integer partitions of n whose unsigned differences have the same GCD as the GCD of their parts all minus 1.
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4
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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
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OFFSET
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0,4
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COMMENTS
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Zeros are ignored when computing GCD, and the empty set has GCD 0.
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LINKS
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EXAMPLE
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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)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], GCD@@Differences[#]==GCD@@(#-1)&]], {n, 0, 30}]
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CROSSREFS
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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.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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