A226169 Niven numbers when expressed in bases 1 through 10.

1, 2, 4, 6, 24, 40, 48, 72, 120, 144, 180, 216, 252, 288, 324, 336, 360, 432, 504, 576, 648, 720, 756, 780, 840, 960, 1008, 1056, 1080, 1092, 1200, 1260, 1296, 1344, 1380, 1440, 1512, 1584, 1620, 1680, 1728, 1764, 1800, 1944, 2016, 2196, 2304, 2352, 2448

Offset: 1

Author

Sergio Pimentel, May 29 2013

Keywords

• nonn
• base
• easy

Comments

The first 10 odd terms greater than 1 are a(1151) = 543375, 5329233, 18640125, 19178775, 23186625, 30131535, 35026425, 36797775, 46101825, 51856875. - Giovanni Resta, Jun 01 2013

Examples

			Example: 336 is in the sequence because the sum of digits of 336 when expressed in bases 1 through 10 is: 336, 3, 4, 3, 8, 6, 12, 7, 8, 12; and 336 is divisible by all these numbers.  In this particular example 336 keeps this property in bases 11, 12 and 13, but not 14.
		

Links

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

Crossrefs

Cf. A049445, A118363, A005349, A144261, A144262.

Programs

Mathematica

Select[Range[10^4], Catch[Do[If[Mod[#, Total@IntegerDigits[#, b]] > 0, Throw@ False], {b, 2, 10}]; True] &] (* Giovanni Resta, May 29 2013 *)
t = Table[b = 2; While[s = Total[IntegerDigits[n, b]]; s < n && Mod[n, s] == 0, b++]; If[s == n, b = 0]; b, {n, 2000}]; Flatten[Position[t, ?(# == 0 || # > 10 &)]] (* _T. D. Noe, May 30 2013 *)

Extensions

Missing a(17) and a(35)-a(49) from Giovanni Resta, May 29 2013