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A114136 Numbers k such that k divides the sum of digits of all numbers from 1 to k. 0
1, 3, 5, 7, 9, 18, 21, 24, 38, 58, 78, 98, 298, 498, 501, 537, 698, 702, 707, 711, 716, 898, 1141, 1197, 1501, 1557, 1998, 2703, 2706, 2712, 2715, 3998, 4502, 4509, 4529, 4536, 5998, 7998, 8001, 8097, 9998, 29998, 36001, 36297, 49998, 54504, 54507, 54510 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) | A037123(a(n)). Sequence is infinite, including 10^(2m)-2 for all m >= 1. For each m >= 1, there is at least one n with A037123(a(n))/a(n) = m.

Number of terms < 10^m for m >= 1: 5, 12, 22, 41, 58, 79, 105, 128, 176, 202, ..., . - Robert G. Wilson v, Jul 06 2018

Certain number forms appear repeatedly: 1(9e)8, 3(9e)8, 5(9e)8, 7(9e)8, 9(9e)8, 2(9o)8, 4(9o)8, 6(9o)8, 8(9o)8; where e represents an even number of times and o an odd number of times. - Robert G. Wilson v, Jul 06 2018

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..202

MAPLE

P:=proc(n) local i, k, w, sp; sp:=0; for i from 1 by 1 to n do w:=0; k:=i; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; sp:=sp+w; if sp/i=trunc(sp/i) then print(i); fi; od; end: P(5000); # Paolo P. Lava, Jul 30 2007

MATHEMATICA

lst = {}; k = 1; s = 0; While[k < 10001, If[ Mod[s += Plus @@ IntegerDigits@k, k++] == 0, AppendTo[lst, k -1]]]; lst (* Robert G. Wilson v, Jul 06 2018 *)

PROG

(PARI) isok(n) = (sum(k=1, n, sumdigits(k)) % n) == 0; \\ Michel Marcus, Jul 16 2018

CROSSREFS

Cf. A037123.

Sequence in context: A212292 A270837 A057482 * A025072 A083107 A003052

Adjacent sequences:  A114133 A114134 A114135 * A114137 A114138 A114139

KEYWORD

base,nonn,changed

AUTHOR

David W. Wilson, Feb 02 2006

STATUS

approved

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Last modified July 23 06:17 EDT 2018. Contains 312921 sequences. (Running on oeis4.)