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

1,2

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

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A261832 A141526 A370418 * A343728 A261746 A319575

Adjacent sequences: A226166 A226167 A226168 * A226170 A226171 A226172

Keyword

nonn,base,easy

Author

Sergio Pimentel, May 29 2013

Extensions

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

Status

approved