A087143 Numbers n such that sum of digits of n is divisible by digital root of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 44, 45, 46, 48, 50, 51, 52, 53, 54, 55, 57, 60, 61, 62, 63, 64, 66, 70, 71, 72, 73, 75, 80, 81, 82, 84, 90

Offset

1,2

Comments

A007953(a(n)) mod A010888(a(n)) = 0; multiples of 9 are a subsequence (A008591, n>0).

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Example

84 is a term because 12 (its sum of digits) is divisible by 3 (its digital root).

Maple

A087143 := proc(n) option remember: local k: if(n=1)then return 1:fi: for k from procname(n-1)+1 do if(add(d, d=convert(k, base, 10)) mod (((k-1) mod 9) + 1) = 0)then return k: fi: od: end: seq(A087143(n), n=1..100); # Nathaniel Johnston, May 05 2011

Mathematica

sddrQ[n_]:=Module[{sd=Total[IntegerDigits[n]], dr}, dr=sd; While[dr>9, dr= Total[ IntegerDigits[dr]]]; Divisible[sd, dr]]; Select[Range[100], sddrQ] (* Harvey P. Dale, May 22 2013 *)

Prog

(PARI) is(n)=sumdigits(n)%((n-1)%9+1) == 0 \\ Charles R Greathouse IV, Oct 13 2022

Crossrefs

Complement of A087144.

Cf. A010888, A064807.

Sequence in context: A194906 A160546 A356944 * A080683 A174228 A197640

Adjacent sequences: A087140 A087141 A087142 * A087144 A087145 A087146

Keyword

nonn,easy,base

Author

Reinhard Zumkeller, Aug 18 2003

Status

approved