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 A303138 Regular triangle where T(n,k) is the number of strict integer partitions of n with greatest common divisor k. 7
 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 2, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 4, 0, 0, 0, 0, 0, 1, 4, 1, 0, 0, 0, 0, 0, 1, 6, 0, 1, 0, 0, 0, 0, 0, 1, 7, 2, 0, 0, 0, 0, 0, 0, 0, 1, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 10, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 17, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 23, 0, 2, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,11 LINKS FORMULA If k divides n, T(n,k) = A078374(n/k); otherwise T(n,k) = 0. EXAMPLE Triangle begins: 01:   1 02:   0  1 03:   1  0  1 04:   1  0  0  1 05:   2  0  0  0  1 06:   2  1  0  0  0  1 07:   4  0  0  0  0  0  1 08:   4  1  0  0  0  0  0  1 09:   6  0  1  0  0  0  0  0  1 10:   7  2  0  0  0  0  0  0  0  1 11:  11  0  0  0  0  0  0  0  0  0  1 12:  10  2  1  1  0  0  0  0  0  0  0  1 13:  17  0  0  0  0  0  0  0  0  0  0  0  1 14:  17  4  0  0  0  0  0  0  0  0  0  0  0  1 15:  23  0  2  0  1  0  0  0  0  0  0  0  0  0  1 The strict partitions counted in row 12 are the following. T(12,1) = 10: (11,1) (9,2,1) (8,3,1) (7,5) (7,4,1) (7,3,2) (6,5,1) (6,3,2,1) (5,4,3) (5,4,2,1) T(12,2) = 2:  (10,2) (6,4,2) T(12,3) = 1:  (9,3) T(12,4) = 1:  (8,4) T(12,12) = 1: (12) MATHEMATICA Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&GCD@@#===k&]], {n, 15}, {k, n}] CROSSREFS First column is A078374. Second column at even indices is same as first column. Row sums are A000009. Row sums with first column removed are A303280. Cf. A000009, A000837, A018783, A051424, A117408, A168532, A289508, A289509, A298748, A300486, A302698, A302796, A303139, A303140, A303280. Sequence in context: A060016 A117408 A228360 * A276205 A244966 A079100 Adjacent sequences:  A303135 A303136 A303137 * A303139 A303140 A303141 KEYWORD nonn,tabl AUTHOR Gus Wiseman, Apr 19 2018 STATUS approved

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Last modified March 21 22:19 EDT 2019. Contains 321382 sequences. (Running on oeis4.)