A253205 Natural numbers n such that n-1 is divisible by the sum of the decimal digits of n.

1, 10, 11, 13, 17, 41, 43, 56, 91, 97, 100, 101, 106, 121, 131, 155, 157, 161, 181, 188, 221, 232, 233, 239, 254, 271, 274, 301, 305, 311, 353, 361, 365, 385, 391, 401, 421, 451, 452, 491, 494, 508, 521, 529, 541, 551, 599, 610, 617, 625, 631, 647, 650, 673

Offset

1,2

Comments

Numbers of the form 1000...000 and 1000...0001 also belong to A144980.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..10000

Formula

a(n) = A160947(n-1)+1. [discovered by sequencedb.net]. - R. J. Mathar, Jun 24 2021

Example

1-1 = 0 is divisible by 1, hence 1 is in the sequence; 56-1 = 55 is divisible by 5+6 = 11, hence 56 is in the sequence.

Maple

with(numtheory): P:=proc(q)local a, b, k, n;
for n from 1 to q do a:=n; b:=0;
for k from 1 to ilog10(n)+1 do b:=b+(a mod 10); a:=trunc(a/10); od;
if type((n-1)/b, integer) then print(n); fi; od; end: P(10^5);

Mathematica

Select[Range[10^3], Mod[#-1, Total[IntegerDigits[#]]]==0&] (* Ivan N. Ianakiev, Mar 25 2015 *)

Prog

(PARI) lista(nn) = for (n=1, nn, if ((n-1) % sumdigits(n) == 0, print1(n, ", "))); \\ Michel Marcus, Mar 25 2015

Crossrefs

Cf. A005349, A144967, A144980.

Sequence in context: A216836 A188165 A125588 * A095038 A085186 A345289

Adjacent sequences: A253202 A253203 A253204 * A253206 A253207 A253208

Keyword

nonn,base,easy

Author

Paolo P. Lava, Mar 25 2015

Extensions

Missing a(5270) in b-file inserted by Andrew Howroyd, Feb 23 2018

Status

approved