OFFSET
1,2
COMMENTS
From Robert Israel, Jun 29 2018: (Start)
Numbers k such that A037123(k - 1) is divisible by k.
If m is even, then 10^m, 3 * 10^m, 5 * 10^m, 7 * 10^m and 9 * 10^m are included.
If m is odd, then 2 * 10^m, 4 * 10^m, 6 * 10^m, and 8 * 10^m are included. (End)
Is it true that if k is a term then 100 * k is a term?
LINKS
Henry Bottomley, Table of n, a(n) for n = 1..118
EXAMPLE
For n = 7, sum of the digits of the numbers 1 to 6 is 21, which is divisible by 7.
For n = 12, sum of the digits of the numbers 1 to 11 is 48, which is divisible by 12.
For n = 15, sum of the digits of the numbers 1 to 14 is 60, which is divisible by 15.
16 is not in the sequence because the sum of the digits of the numbers 1 to 15 is 66, which is not divisible by 16.
MAPLE
t:= 0: Res:= NULL:
for n from 1 to 10000 do
t:= t + convert(convert(n-1, base, 10), `+`);
if (t/n)::integer then Res:= Res, n fi
od:
Res; # Robert Israel, Jun 29 2018
MATHEMATICA
s = 0; Reap[Do[If[Mod[s, n] == 0, Sow[n]]; s += Plus @@ IntegerDigits@n, {n, 10000}]][[2, 1]] (* Giovanni Resta, Jun 29 2018 *)
PROG
(PARI) sumsod(n) = sum(i=1, n, sumdigits(i))
is(n) = sumsod(n-1)%n==0 \\ Felix Fröhlich, Jun 29 2018
(PARI) upto(n) = my(s=0, res=List()); for(i=0, n, s += vecsum(digits(i)); if(s%(i+1)==0, listput(res, i+1))); res \\ David A. Corneth, Jun 29 2018
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Debapriyay Mukhopadhyay, Jun 29 2018
EXTENSIONS
More terms from Felix Fröhlich, Jun 29 2018
STATUS
approved