A333622 - OEIS

%I #11 Aug 25 2023 08:40:22

%S 1,2,3,4,14,22,24,27,33,36,52,72,91,92,100,135,150,187,221,231,310,

%T 323,448,481,493,494,589,663,708,754,816,884,893,897,946,1080,1155,

%U 1159,1178,1200,1357,1462,1475,1518,1530,1536,1550,1702,1710,1836,1972,1978,2231

%N Numbers k such that k is divisible by the sum of digits of all the divisors of k in factorial base (A319712).

%H Amiram Eldar, <a href="/A333622/b333622.txt">Table of n, a(n) for n = 1..10000</a>

%e 14 is a term since its divisors are {1, 2, 7, 14}, their representations in factorial base (A007623) are {1, 10, 101, 210}, and their sum of sums of digits is 1 + (1 + 0) + (1 + 0 + 1) + (2 + 1 + 0) = 7 which is a divisor of 14.

%t fctDigSum[n_] := Module[{s=0, i=2, k=n}, While[k > 0, k = Floor[n/i!]; s = s + (i-1)*k; i++]; n-s]; fctDivDigDum[n_] := DivisorSum[n, fctDigSum[#] &]; Select[Range[10^3], Divisible[#, fctDivDigDum[#]] &] (* after _Jean-François Alcover_ at A034968 *)

%Y Cf. A007623, A034968, A093705, A319712, A333617, A333619, A333620, A333623.

%K nonn,base

%O 1,2

%A _Amiram Eldar_, Mar 29 2020