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A098965
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Number of integer partitions of n into distinct parts > 1 with a part dividing all the other parts.
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12
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0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 5, 1, 3, 3, 5, 1, 7, 1, 8, 4, 6, 1, 15, 2, 9, 5, 14, 1, 22, 1, 20, 7, 18, 4, 36, 1, 26, 10, 40, 1, 51, 1, 48, 18, 49, 1, 86, 3, 73, 19, 86, 1, 117, 7, 120, 27, 120, 1, 196, 1, 160, 42, 201, 10, 259, 1, 258, 50, 292, 1, 407, 1, 357, 81, 431, 8, 548, 1, 577
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OFFSET
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1,6
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COMMENTS
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If n > 0, we can assume this part is the smallest. - Gus Wiseman, Apr 18 2021
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LINKS
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FORMULA
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a(n) = Sum_{d|n, d<n} A025147(d-1).
G.f.: Sum_{k>=2} (x^k*Product_{i>=2}(1 + x^(k*i))).
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MATHEMATICA
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Take[ CoefficientList[ Expand[ Sum[x^k*Product[1 + x^(k*i), {i, 2, 92}], {k, 2, 92}]], x], {2, 81}] (* Robert G. Wilson v, Nov 01 2004 *)
Table[If[n==0, 0, Length[Select[IntegerPartitions[n], !MemberQ[#, 1]&&UnsameQ@@#&&And@@IntegerQ/@(#/Min@@#)&]]], {n, 0, 30}] (* Gus Wiseman, Apr 18 2021 *)
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CROSSREFS
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The non-strict version with 1's allowed is A083710.
The version with 1's allowed is A097986.
The Heinz numbers of these partitions are the odd terms of A339563.
The strict complement is counted by A341450.
A000070 counts partitions with a selected part.
A006128 counts partitions with a selected position.
A015723 counts strict partitions with a selected part.
A167865 counts strict chains of divisors > 1 summing to n.
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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