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A303140
Number of strict integer partitions of n with at least two but not all parts having a common divisor greater than 1.
15
0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 4, 2, 8, 7, 14, 14, 21, 18, 33, 32, 50, 54, 72, 67, 103, 110, 145, 155, 201, 196, 271, 293, 372, 400, 493, 512, 647, 704, 858, 924, 1115, 1167, 1436, 1560, 1854, 2022, 2368, 2510, 3005, 3255, 3804, 4144, 4792, 5116, 5989, 6514, 7486
OFFSET
1,9
EXAMPLE
The a(14) = 7 partitions are (932), (8321), (7421), (653), (6521), (6431), (5432).
MATHEMATICA
Table[Select[IntegerPartitions[n], UnsameQ@@#&&!CoprimeQ@@#&&GCD@@#===1&]//Length, {n, 20}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 19 2018
STATUS
approved