OFFSET
1,72
LINKS
FORMULA
EXAMPLE
1 can be factored just one way, as 1*1, and thus a(1) = 1.
4 can be factored as 2*2, and thus also a(4) = 1, and generally for all perfect squares k, a(k) >= 1.
14 can be factored as 2*7, but as A007623(2) = 2 and A007623(7) = 101, with different number of digits in factorial base (and 1*14 fares even less well), a(14) = 0.
72 can be factored to two divisors so that the factorial base representations are of equal length as 6*12 or 8*9 (where the corresponding factorial base representations are "100" * "200" and "110" * "111"), thus a(72) = 2.
120 can be similarly factored as 6*20 ("100" * "310"), 8*15 ("110" * "211") and 10*12 ("120" * "200"), thus a(120) = 3.
MATHEMATICA
r = Most@ Reverse@ Range@ 10; Map[Length, Table[Flatten@ Map[Differences@ IntegerLength[#, MixedRadix@ r] &, Transpose@ {#, n/#}] &@ TakeWhile[Divisors@ n, # <= Sqrt@ n &], {n, 120}] /. k_ /; k > 0 -> Nothing] (* Michael De Vlieger, Dec 30 2015, Version 10.2 *)
PROG
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Dec 28 2015
STATUS
approved