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A077563
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Number of partitions into two parts which have different prime signatures.
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3
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0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 5, 4, 4, 5, 6, 4, 8, 6, 8, 6, 8, 8, 11, 7, 10, 10, 12, 10, 12, 10, 13, 10, 15, 12, 15, 10, 17, 16, 17, 13, 18, 16, 18, 16, 19, 18, 21, 13, 20, 19, 25, 20, 23, 19, 24, 20, 25, 24, 27, 19, 24, 26, 28, 21, 28, 25, 30, 26, 31, 26, 32, 19, 30, 30, 33, 30
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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COMMENTS
| The 'prime signature' of n is the sorted list of exponents in the prime factorization of n.
Does lim n->infinity a(n)/n exist? If not, what are the limsup and liminf of a(n)/n?
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EXAMPLE
| a(9) = 3; the partitions are 8+1, 6+3 and 5+4.
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MATHEMATICA
| sig[n_] := Sort[Last/@FactorInteger[n]]; a[n_] := Length[Select[Range[Floor[n/2]], sig[ # ]!=sig[n-# ]&]]
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CROSSREFS
| Cf. A077564.
Sequence in context: A008997 A005851 A139821 * A055256 A029147 A029097
Adjacent sequences: A077560 A077561 A077562 * A077564 A077565 A077566
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 11 2002
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Nov 11 2002
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