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A111306
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d_12(n), tau_12(n), number of ordered factorizations of n as n = rstuvwxyzabc (12-factorizations).
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6
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1, 12, 12, 78, 12, 144, 12, 364, 78, 144, 12, 936, 12, 144, 144, 1365, 12, 936, 12, 936, 144, 144, 12, 4368, 78, 144, 364, 936, 12, 1728, 12, 4368, 144, 144, 144, 6084, 12, 144, 144, 4368, 12, 1728, 12, 936, 936, 144, 12, 16380, 78, 936, 144, 936, 12, 4368, 144
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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+11,11). - Amiram Eldar, Sep 13 2020
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MAPLE
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b:= proc(n, k) option remember; `if`(k=1, 1,
add(b(d, k-1), d=numtheory[divisors](n)))
end:
a:= n-> b(n, 12):
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MATHEMATICA
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tau[k_, 1]:=1; tau[k_, n_]:=Times@@(Binomial[#+k-1, k-1]&/@FactorInteger[n][[All, 2]]); Table[tau[12, n], {n, 1000}] (* Enrique Pérez Herrero, Jan 17 2013 *)
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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, p, sumdiv(p, q, sumdiv(q, r, sumdiv(r, 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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