A234814 Numbers that are divisible by their digital sum but not by their digital root.

195, 209, 247, 266, 285, 375, 392, 407, 465, 476, 481, 518, 555, 592, 605, 629, 644, 645, 715, 735, 736, 782, 803, 825, 880, 915, 935, 1066, 1095, 1148, 1168, 1183, 1185, 1274, 1275, 1365, 1394, 1417, 1455, 1526, 1534, 1545, 1547, 1635, 1651, 1652, 1679, 1725, 1744, 1815, 1853, 1886, 1898, 1904, 1905

Offset: 1

Author

Mihir Mathur, Dec 31 2013

Keywords

• nonn
• base

Comments

These are the Harshad numbers which are missing from A234474.

Examples

			195 is a term as it is divisible by its digital sum i.e. 15 but not by its digital root i.e. 6.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Harshad number.

Crossrefs

Cf. A005349, A234474.

Cf. A064807, A007953, A010888.

Programs

Haskell

a234814 n = a234814_list !! (n-1)
a234814_list = filter (\x -> x `mod` a007953 x == 0 &&
                             x `mod` a010888 x /= 0) [1..]
-- Reinhard Zumkeller, Mar 04 2014

Mathematica

Select[Range@1905, Mod[#, 1 + Mod[#-1, 9]] > 0 && Mod[#, Plus@@ IntegerDigits@ #] == 0 &] (* Giovanni Resta, Jan 03 2014 *)