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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Zeros are ignored when computing GCD, and the empty set has GCD 0. LINKS 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. Cf. A000837, A018783, A175342, A279945, A289508, A328168, A328169. Sequence in context: A182708 A304709 A183558 * A294916 A233423 A328024 Adjacent sequences:  A328161 A328162 A328163 * A328165 A328166 A328167 KEYWORD nonn AUTHOR Gus Wiseman, Oct 07 2019 STATUS approved

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Last modified January 29 01:49 EST 2020. Contains 331328 sequences. (Running on oeis4.)