A319711 Sum of A034968(d) over proper divisors d of n, where A034968 gives the sum of digits in factorial base.

0, 1, 1, 2, 1, 4, 1, 4, 3, 5, 1, 7, 1, 4, 6, 6, 1, 8, 1, 10, 5, 6, 1, 11, 4, 5, 6, 9, 1, 15, 1, 10, 7, 7, 6, 15, 1, 6, 6, 16, 1, 15, 1, 13, 13, 8, 1, 16, 3, 10, 8, 9, 1, 14, 8, 14, 7, 6, 1, 25, 1, 5, 13, 13, 7, 18, 1, 13, 9, 18, 1, 21, 1, 6, 12, 12, 7, 15, 1, 25, 9, 8, 1, 26, 9, 7, 7, 20, 1, 29, 6, 16, 6, 9, 8, 21, 1, 10, 14, 19, 1, 18, 1, 15, 22

Offset: 1

Author

Antti Karttunen, Oct 02 2018

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to factorial base representation.

Crossrefs

Cf. A034968, A319712, A319713.

Programs

Mathematica

d[n_] := Module[{k = n, m = 2, s = 0, r}, While[{k, r} = QuotientRemainder[k, m]; k != 0 || r != 0, s += r; m++]; s]; a[n_] := DivisorSum[n, d[#] &, # < n &]; Array[a, 100] (* Amiram Eldar, Mar 05 2024 *)

PARI

A034968(n) = { my(s=0, b=2, d); while(n, d = (n%b); s += d; n = (n-d)/b; b++); (s); };
A319711(n) = sumdiv(n,d,(dA034968(d));

Formula

a(n) = Sum_{d|n, dA034968(d).

a(n) = A319712(n) - A034968(n).