A333702 Numbers k such that k divides the sum of digits in factorial base of all numbers from 1 to k.

1, 2, 10, 22, 25, 29, 33, 70, 118, 358, 598, 1438, 1803, 1819, 2878, 2881, 2997, 4318, 4322, 4388, 10078, 20158, 21967, 21971, 21975, 30238, 30241, 30837, 40318, 120958, 141121, 142557, 201598, 214563, 214675, 282238, 362878, 649446, 649504, 1088638, 1303204, 1303314

Offset: 1

Author

Amiram Eldar, Apr 02 2020

Keywords

• nonn
• base

Comments

The corresponding quotients are 1, 1, 2, 3, 3, 3, 3, 4, 5, ...

Examples

			10 is a term since the sum of digits in factorial base (A034968) of k from 1 to 10 is 1 + 1 + 2 + 2 + 3 + 1 + 2 + 2 + 3 + 3 = 20, which is divisible by 10.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..137
• Index entries for sequences related to factorial base representation.

Crossrefs

Cf. A007623, A034968, A368342.

Cf. A095376, A114136, A333703, A333704, A333705.

Programs

Mathematica

f[n_] := Module[{s=0, i=2, k=n}, While[k > 0, k = Floor[n/i!]; s = s + (i-1)*k; i++]; n-s]; seq = {}; s = 0; Do[s += f[n]; If[Divisible[s, n], AppendTo[seq, n]], {n, 1, 10^5}]; seq (* after Jean-François Alcover at A034968 *)