A234474 -id:A234474 - cp's OEIS frontend

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

Mihir Mathur, Dec 31 2013

These are the Harshad numbers which are missing from A234474.

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

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

Cf. A005349, A234474.

Cf. A064807, A007953, A010888.

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

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

A285829 Numbers n such that, for any i and j with i >= j >= 0, ds^i(n) divides ds^j(n) (where ds^k denotes the k-th iteration of the digital sum).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 102, 108, 110, 111, 112, 114, 117, 120, 126, 132, 133, 135, 140, 144, 150, 152, 153, 156, 162, 171, 180, 190, 192, 198, 200, 201, 204, 207, 210, 216, 220, 222, 224, 225, 228, 230, 234, 240, 243, 252, 261, 264, 270, 280, 288, 300, 306, 312

Offset: 1

Rémy Sigrist, Apr 27 2017

All terms are Niven numbers (A005349).
All terms belongs to A234474; the first difference occurs at index 81: a(81) = 312 whereas A234474(81) = 308.
All powers of 10 belong to the sequence, hence the sequence is infinite.

			The digital sum of 312 is 6, and it divides 312; the digital sum of 6 is 6; hence 312 appears in the sequence.
The digital sum of 308 is 11, which divides 308; however the digital sum of 11 is 2, which does not divide 11; hence 308 is not in the sequence.

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Cf. A005349, A234474.

is(n) = my (d=sumdigits(n)); if (n==d, return (1)); if (n%d, return (0)); return (is(d))

cp's OEIS Frontend

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

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