A319712 Sum of A034968(d) over divisors d of n, where A034968 gives the sum of digits in factorial base.

1, 2, 3, 4, 4, 5, 3, 6, 6, 8, 5, 9, 4, 7, 10, 10, 6, 11, 5, 14, 10, 11, 7, 12, 6, 7, 9, 12, 5, 17, 4, 13, 11, 11, 11, 18, 5, 10, 11, 21, 7, 19, 6, 18, 19, 14, 8, 18, 6, 13, 12, 13, 6, 17, 12, 18, 12, 11, 7, 29, 6, 10, 19, 19, 14, 23, 7, 19, 16, 25, 9, 24, 5, 10, 17, 17, 13, 19, 6, 30, 15, 14, 8, 31, 15, 13, 14, 27, 9, 35, 13, 23, 14, 17, 17

Offset: 1

Author

Antti Karttunen, Oct 02 2018

Keywords

• nonn
• base

Comments

Inverse Möbius transform of A034968.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..40320
• Index entries for sequences related to factorial base representation.

Crossrefs

Cf. A034968, A319711, A319715.

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[#] &]; Array[a, 100] (* Amiram Eldar, Feb 14 2024 *)

PARI

A034968(n) = { my(s=0, b=2, d); while(n, d = (n%b); s += d; n = (n-d)/b; b++); (s); };
A319712(n) = sumdiv(n,d,A034968(d));

Formula

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

a(n) = A319711(n) + A034968(n).