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A328163
Number of integer partitions of n whose unsigned differences have a different GCD than the GCD of their parts all minus 1.
6
0, 0, 1, 1, 2, 1, 4, 2, 5, 5, 9, 5, 15, 9, 19, 16, 28, 16, 44, 21, 55, 38, 73, 34, 109, 46, 130, 73, 170, 66, 251, 78, 287, 137, 364, 119, 522, 135, 590, 236, 759, 190, 1042, 219, 1175, 425, 1460, 306, 2006, 347, 2277, 671, 2780, 471, 3734, 584, 4197, 1087
OFFSET
0,5
COMMENTS
Zeros are ignored when computing GCD, and the empty set has GCD 0.
EXAMPLE
The a(2) = 1 through a(12) = 15 partitions (A = 10, B = 11, C = 12):
(2) (3) (4) (5) (6) (7) (8) (9) (A) (B) (C)
(22) (33) (52) (44) (63) (55) (83) (66)
(42) (62) (72) (64) (92) (84)
(222) (422) (333) (73) (722) (93)
(2222) (522) (82) (5222) (A2)
(442) (444)
(622) (552)
(4222) (633)
(22222) (642)
(822)
(3333)
(4422)
(6222)
(42222)
(222222)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], GCD@@Differences[#]!=GCD@@(#-1)&]], {n, 0, 30}]
CROSSREFS
The complement to these partitions is counted by A328164.
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: A161077 A339220 A161293 * A217916 A057923 A147763
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 07 2019
STATUS
approved