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A061200
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tau_5(n) = number of ordered 5-factorizations of n.
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15
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1, 5, 5, 15, 5, 25, 5, 35, 15, 25, 5, 75, 5, 25, 25, 70, 5, 75, 5, 75, 25, 25, 5, 175, 15, 25, 35, 75, 5, 125, 5, 126, 25, 25, 25, 225, 5, 25, 25, 175, 5, 125, 5, 75, 75, 25, 5, 350, 15, 75, 25, 75, 5, 175, 25, 175, 25, 25, 5, 375, 5, 25, 75, 210, 25, 125, 5, 75, 25, 125, 5
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| tau_k(n) = |{(x_1,x_2,...,x_k): x_1*x_2*...*x_k=n}|, number of ordered k-factorizations of n. tau_k(p^m)=(-1)^(k-1)*binomial(-m-1,k-1), p -prime. limit(tau_k(n)/n^epsilon, n=infinity)=0, for any epsilon>0.
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FORMULA
| tau_k(n)=Sum_{d|n} tau_(k-1)(d), tau_1(n)=1. Dirichlet g.f.: (zeta(s))^k. For explicit formula, cf. A007425.
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MATHEMATICA
| tau[n_, 1] = 1; tau[n_, k_] := tau[n, k] = Plus @@ (tau[ #, k - 1] & /@ Divisors[n]); Table[ tau[n, 5], {n, 77}] (* Robert G. Wilson v *)
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PROG
| (PARI) for(n=1, 100, print1(sumdiv(n, k, sumdiv(k, x, sumdiv(x, y, numdiv(y)))), ", "))
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CROSSREFS
| Cf. tau_2(n): A000005, tau_3(n): A007425, tau_4(n): A007426, tau_6(n): A034695, (unordered) 2-factorization of n: A038548, (unordered) 3-factorization of n: A034836, A001055, A006218, A061201-A061204.
Sequence in context: A192987 A062367 A168418 * A050350 A196060 A147266
Adjacent sequences: A061197 A061198 A061199 * A061201 A061202 A061203
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KEYWORD
| easy,nonn,mult
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 21 2001
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