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A333702 Numbers k such that k divides the sum of digits in factorial base of all numbers from 1 to k. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..42.

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A007623, A034968, A095376, A114136, A333703, A333704, A333705.

Sequence in context: A138298 A303294 A302566 * A119153 A339486 A273993

Adjacent sequences:  A333699 A333700 A333701 * A333703 A333704 A333705

KEYWORD

nonn

AUTHOR

Amiram Eldar, Apr 02 2020

STATUS

approved

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Last modified September 18 12:35 EDT 2021. Contains 347527 sequences. (Running on oeis4.)