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Search: id:A077564
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| A077564 |
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Number of partitions of n into parts with distinct prime signatures. |
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+0
4
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| 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 8, 10, 10, 11, 14, 14, 19, 22, 22, 25, 30, 34, 38, 40, 46, 54, 60, 63, 74, 81, 85, 91, 108, 118, 126, 134, 153, 173, 180, 186, 214, 236, 245, 262, 301, 326, 338, 355, 395, 437, 461, 476, 540, 592, 610, 649, 717, 768, 811, 853, 943, 1039
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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The 'prime signature' of n is the sorted list of exponents in the prime factorization of n.
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EXAMPLE
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a(7) = 4. The partitions are 7, 6+1, 4+3, 4+2+1. (5+2, 3+2+2, ... are not counted.)
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MATHEMATICA
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sig[n_] := Sort[Last/@FactorInteger[n]]; f[n_, m_] := Module[{sm}, If[n>m(m+1)/2||n<0, Return[{}]]; If[n==0, Return[{{}}]]; sm=sig[m]; f[n, m]=Union[f[n, m-1], Prepend[ #, m]&/@Select[f[n-m, m-1], !MemberQ[sig/@#, sm]&]]]; a[n_] := Length[f[n, n]] (* f[n, m] is list of partitions of n into parts <= m with distinct prime signatures *)
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CROSSREFS
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Cf. A077563.
Sequence in context: A143644 A104410 A018048 this_sequence A088044 A029051 A079398
Adjacent sequences: A077561 A077562 A077563 this_sequence A077565 A077566 A077567
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 11 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Nov 11 2002
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