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A111219
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d_9(n), tau_9(n), number of ordered factorizations of n as n = rstuvwxyz (9-factorizations).
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7
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1, 9, 9, 45, 9, 81, 9, 165, 45, 81, 9, 405, 9, 81, 81, 495, 9, 405, 9, 405, 81, 81, 9, 1485, 45, 81, 165, 405, 9, 729, 9, 1287, 81, 81, 81, 2025, 9, 81, 81, 1485, 9, 729, 9, 405, 405, 81, 9, 4455, 45, 405, 81, 405, 9, 1485, 81, 1485, 81, 81, 9, 3645, 9, 81, 405, 3003, 81
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OFFSET
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1,2
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LINKS
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FORMULA
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Multiplicative with a(p^e) = binomial(e+8,8). - Amiram Eldar, Sep 13 2020
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MATHEMATICA
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tau[n_, 1] = 1; tau[n_, k_] := tau[n, k] = Plus @@ (tau[ #, k - 1] & /@ Divisors[n]); Table[ tau[n, 9], {n, 65}] (* Robert G. Wilson v, Nov 02 2005 *)
tau[1, k_] := 1; tau[n_, k_] := Times @@ (Binomial[Last[#]+k-1, k-1]& /@ FactorInteger[n]); Table[tau[n, 9], {n, 1, 100}] (* Amiram Eldar, Sep 13 2020 *)
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PROG
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(PARI) for(n=1, 100, print1(sumdiv(n, i, sumdiv(i, j, sumdiv(j, k, sumdiv(k, l, sumdiv(l, m, sumdiv(m, o, sumdiv(o, x, numdiv(x)))))))), ", "))
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CROSSREFS
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KEYWORD
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mult,nonn
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AUTHOR
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STATUS
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approved
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