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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

Table of n, a(n) for n=0..47.

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.)