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Search: id:A106244
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| A106244 |
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Number of partitions into distinct prime powers. |
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+0
8
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| 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 17, 19, 21, 24, 27, 30, 33, 37, 41, 46, 50, 56, 62, 68, 75, 82, 91, 99, 108, 118, 129, 141, 152, 166, 180, 196, 211, 229, 248, 267, 288, 310, 335, 360, 387, 415, 447, 479, 513, 549, 589, 630, 672, 719, 768, 820, 873, 930
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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A054685(n) < a(n) < A023893(n) for n>2.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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a(n) = A054685(n-1)+A054685(n). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 28 2005
G.f.=(1+x)*Product(Product(1+x^(p(k)^j), j=1..infinity),k=1..infinity), where p(k) is the k-th prime (offset 0). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 27 2007
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EXAMPLE
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a(10) = #{3^2+1,2^3+2,7+3,7+2+1,5+2^2+1,5+3+2,2^2+3+2+1} = 7.
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MAPLE
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g:=(1+x)*(product(product(1+x^(ithprime(k)^j), j=1..5), k=1..20)): gser:=series(g, x=0, 68): seq(coeff(gser, x, n), n=1..63); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 27 2007
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CROSSREFS
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Cf. A000586, A000607, A000961.
Cf. A062051, A105420, A131996.
Sequence in context: A011881 A076678 A029024 this_sequence A029023 A140952 A096911
Adjacent sequences: A106241 A106242 A106243 this_sequence A106245 A106246 A106247
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 26 2005
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