A333703 Numbers k such that k divides the sum of digits in primorial base of all numbers from 1 to k.

1, 2, 10, 22, 58, 62, 63, 64, 66, 67, 68, 118, 178, 418, 838, 1258, 1264, 1265, 1277, 1278, 1678, 2098, 4618, 9238, 10508, 10509, 10510, 10512, 10513, 10514, 13858, 14704, 14754, 18478, 23098, 23102, 23276, 27718, 60058, 120118, 138602, 139016, 139024, 139134

Offset: 1

Author

Amiram Eldar, Apr 02 2020

Keywords

• nonn
• base

Comments

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

Examples

			10 is a term since the sum of digits in primorial base (A276150) 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..136
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A049345, A276150, A095376, A114136, A333702, A333704, A333705.

Programs

Mathematica

max = 10; bases = Prime@Range[max, 1, -1]; nmax = Times @@ bases - 1; s[n_] := Plus @@ IntegerDigits[n, MixedRadix[bases]]; seq = {}; sum = 0; Do[sum += s[n]; If[Divisible[sum, n], AppendTo[seq, n]], {n, 1, 10^6}]; seq