OFFSET
1,4
COMMENTS
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
FORMULA
a(n) = A319686(n)-1.
EXAMPLE
The proper divisors of 112 are [1, 2, 4, 7, 8, 14, 16, 28, 56]. Applying arithmetic derivative A003415 to these, we obtain values [0, 1, 4, 1, 12, 9, 32, 32, 92], of which only 7 are distinct: 0, 1, 4, 9, 12, 32, and 92, thus a(112) = 7.
MATHEMATICA
d[0] = d[1] = 0; d[n_] := d[n] = n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := CountDistinct[d /@ Most[Divisors[n]]]; Array[a, 100] (* Amiram Eldar, Apr 17 2024 *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 02 2018
STATUS
approved