login
A254578
Number of ordered factorizations into distinct factors.
5
1, 1, 1, 1, 1, 3, 1, 3, 1, 3, 1, 5, 1, 3, 3, 3, 1, 5, 1, 5, 3, 3, 1, 13, 1, 3, 3, 5, 1, 13, 1, 5, 3, 3, 3, 13, 1, 3, 3, 13, 1, 13, 1, 5, 5, 3, 1, 21, 1, 5, 3, 5, 1, 13, 3, 13, 3, 3, 1, 29, 1, 3, 5, 11, 3, 13, 1, 5, 3, 13, 1, 29, 1, 3, 5, 5, 3, 13, 1, 21, 3, 3
OFFSET
1,6
LINKS
Arnold Knopfmacher and Michael Mays, Ordered and Unordered Factorizations of Integers, The Mathematica Journal, Vol 10 (1).
EXAMPLE
a(20)=5 because there are 5 ordered factorizations of 20 into distinct factors: 2*10, 4*5, 5*4, 10*2, 20.
MAPLE
with(numtheory):
b:= proc(n, i, p) option remember; `if`(n<=i, (p+1)!, 0)+add(
b(n/d, d-1, p+1), d=select(x->x<=i, divisors(n)minus{1, n}))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=1..100); # Alois P. Heinz, Feb 01 2015
MATHEMATICA
f[n_] := f[n] = Level[Table[Map[Prepend[#, d] &, f[n/d]], {d, Rest[Divisors[n]]}], {2}];
f[1] = {{}};
Map[Length, Map[Select[#, Apply[Unequal, #] &] &, Table[f[n], {n, 1, 60}]]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Feb 01 2015
STATUS
approved