A333622 Numbers k such that k is divisible by the sum of digits of all the divisors of k in factorial base (A319712).

1, 2, 3, 4, 14, 22, 24, 27, 33, 36, 52, 72, 91, 92, 100, 135, 150, 187, 221, 231, 310, 323, 448, 481, 493, 494, 589, 663, 708, 754, 816, 884, 893, 897, 946, 1080, 1155, 1159, 1178, 1200, 1357, 1462, 1475, 1518, 1530, 1536, 1550, 1702, 1710, 1836, 1972, 1978, 2231

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

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.

Mathematica

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 *)

Crossrefs

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

Sequence in context: A295286 A127283 A047193 * A019137 A333623 A317737

Adjacent sequences: A333619 A333620 A333621 * A333623 A333624 A333625

Keyword

nonn,base

Author

Amiram Eldar, Mar 29 2020

Status

approved