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Search: id:A051613
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| A051613 |
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a(n) = partitions of n into powers of distinct primes (1 not considered a power). |
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+0
11
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| 1, 0, 1, 1, 1, 2, 0, 3, 2, 3, 2, 4, 3, 4, 4, 4, 8, 4, 8, 6, 9, 8, 10, 10, 13, 12, 13, 16, 16, 19, 17, 21, 23, 23, 25, 29, 31, 31, 31, 37, 40, 42, 44, 48, 49, 54, 55, 64, 67, 68, 70, 77, 84, 90, 92, 99, 102, 108, 115, 127, 133, 135, 138, 150, 165, 171, 183, 186, 198, 201, 220
(list; graph; listen)
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OFFSET
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0,6
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REFERENCES
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J. Bamberg, G. Cairns and D. Kilminster, The crystallographic restriction, permutations and Goldbach's conjecture, Amer. Math. Monthly, 110 (March 2003), 202-209.
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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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a(n) = number of m such that A008475(m) = n.
G.f.: Prod(p prime, 1 + Sum(k >= 1, x^(p^k))).
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EXAMPLE
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a(16)=8 because we can write 16=2^4=3+13=5+11=3^2+7=2+3+11=2+3^2+5=2^3+3+5=2^2+5+7
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CROSSREFS
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Cf. A023894, A009490, A054685, A008475.
Cf. A106245.
Sequence in context: A118234 A152039 A132623 this_sequence A077961 A077962 A078031
Adjacent sequences: A051610 A051611 A051612 this_sequence A051614 A051615 A051616
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs)
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EXTENSIONS
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Better description from David W. Wilson (davidwwilson(AT)comcast.net), Apr 19, 2000
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