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

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to factorial base representation.

Formula

a(n) = Sum_{d|n, d<n} A034968(d).

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

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 *)

Prog

(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, (d<n)*A034968(d));

Crossrefs

Cf. A034968, A319712, A319713.

Sequence in context: A107457 A112350 A321437 * A319713 A063717 A024994

Adjacent sequences: A319708 A319709 A319710 * A319712 A319713 A319714

Keyword

nonn,base

Author

Antti Karttunen, Oct 02 2018

Status

approved