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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Zeros are ignored when computing GCD, and the empty set has GCD 0.

LINKS

Table of n, a(n) for n=0..57.

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.

Cf. A000837, A018783, A175342, A279945, A289508, A328168, A328169.

Sequence in context: A161077 A339220 A161293 * A217916 A057923 A147763

Adjacent sequences:  A328160 A328161 A328162 * A328164 A328165 A328166

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 07 2019

STATUS

approved

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Last modified January 21 14:37 EST 2022. Contains 350479 sequences. (Running on oeis4.)