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A050369
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Number of ordered factorizations of n into 2 kinds of 2, 3 kinds of 3, ...
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15
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1, 2, 3, 8, 5, 18, 7, 32, 18, 30, 11, 96, 13, 42, 45, 128, 17, 144, 19, 160, 63, 66, 23, 480, 50, 78, 108, 224, 29, 390, 31, 512, 99, 102, 105, 936, 37, 114, 117, 800, 41, 546, 43, 352, 360, 138, 47, 2304, 98, 400, 153, 416, 53, 1080, 165, 1120, 171, 174, 59, 2640
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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Dirichlet g.f.: 1/(2-zeta(s-1)).
a(n) = n*Sum_{d divides n, d<n} a(d)/d, n>1, a(1)=1. - Vladeta Jovovic, Feb 09 2002
Sum_{k=1..n} a(k) ~ -n^(1+r) / ((1+r)*Zeta'(r)), where r = A107311 = 1.728647238998183618135103010297... is the root of the equation Zeta(r) = 2. - Vaclav Kotesovec, Feb 02 2019
G.f. A(x) satisfies: A(x) = x + 2*A(x^2) + 3*A(x^3) + 4*A(x^4) + ... - Ilya Gutkovskiy, May 10 2019
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MATHEMATICA
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a[1]=1; a[n_]:=a[n]=n*Sum[If[d==n, 0, a[d]/d], {d, Divisors[n]}]; Table[a[n], {n, 1, 100}] (* Vaclav Kotesovec, Feb 02 2019 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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