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%I #27 Mar 12 2024 02:40:52
%S 1,2,4,6,24,40,48,72,120,144,180,216,252,288,324,336,360,432,504,576,
%T 648,720,756,780,840,960,1008,1056,1080,1092,1200,1260,1296,1344,1380,
%U 1440,1512,1584,1620,1680,1728,1764,1800,1944,2016,2196,2304,2352,2448
%N Niven numbers when expressed in bases 1 through 10.
%C 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
%H Amiram Eldar, <a href="/A226169/b226169.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%t Select[Range[10^4], Catch[Do[If[Mod[#, Total@IntegerDigits[#, b]] > 0, Throw@ False], {b, 2, 10}]; True] &] (* _Giovanni Resta_, May 29 2013 *)
%t 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 *)
%Y Cf. A049445, A118363, A005349, A144261, A144262.
%K nonn,base,easy
%O 1,2
%A _Sergio Pimentel_, May 29 2013
%E Missing a(17) and a(35)-a(49) from _Giovanni Resta_, May 29 2013
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