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A226169 Niven numbers when expressed in bases 1 through 10. 4
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..49.

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.

MAPLE

P:=proc(n) local k, ok; ok:=1; for k from 2 to 10 do

if frac(n/convert(convert(n, base, k), `+`))>0 then ok:=0; break; fi; od;

if ok=1 then n; fi; end: seq(P(i), i=1..2450); # Paolo P. Lava, Apr 05 2018

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: A086172 A261832 A141526 * A261746 A319575 A318609

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

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Last modified June 6 13:31 EDT 2020. Contains 334827 sequences. (Running on oeis4.)