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Search: id:A000586
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| A000586 |
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Number of partitions of n into distinct primes.
(Formerly M0022 N0004)
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+0
20
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| 1, 0, 1, 1, 0, 2, 0, 2, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 4, 3, 4, 4, 4, 5, 5, 5, 6, 5, 6, 7, 6, 9, 7, 9, 9, 9, 11, 11, 11, 13, 12, 14, 15, 15, 17, 16, 18, 19, 20, 21, 23, 22, 25, 26, 27, 30, 29, 32, 32, 35, 37, 39, 40, 42, 44, 45, 50, 50, 53, 55, 57, 61, 64, 67, 70, 71, 76, 78, 83, 87, 89, 93, 96
(list; graph; listen)
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OFFSET
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0,6
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REFERENCES
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H. Gupta, Partitions into distinct primes, Proc. Nat. Acad. Sci. India, 21 (1955), 185-187.
H. Gupta, Certain averages connected with partitions. Res. Bull. Panjab Univ. no. 124 1957 427-430.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 0..1000
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FORMULA
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G.f.: Product_{k=1..inf} (1+x^prime(k)).
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EXAMPLE
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n=16 has a(16)=3 partitions into distinct prime parts: 16 = 2+3+11 = 3+13 = 5+11.
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MATHEMATICA
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CoefficientList[Series[Product[(1+x^Prime[k]), {k, 24}], {x, 0, Prime[24]}], x]
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CROSSREFS
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Cf. A000041, A070215, A000607.
Cf. A112022.
Sequence in context: A035226 A126043 A112022 this_sequence A029399 A046069 A055651
Adjacent sequences: A000583 A000584 A000585 this_sequence A000587 A000588 A000589
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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