

A268864


Number of integers of the form n*k whose digits sum up to n where 0 <= k <= n^2.


0



1, 1, 1, 3, 2, 2, 8, 4, 6, 52, 9, 8, 34, 11, 15, 47, 18, 22, 195, 23, 9, 77, 32, 22, 57, 9, 15, 160, 11, 11, 0, 7, 4, 0, 3, 0, 4, 6, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET

0,4


COMMENTS

It appears that a(n)=0 for n>39. This has been checked for n<100.
If n has d digits, i.e. 10^(d1) <= n < 10^d, then k*n <= n^3 has at most 3*d digits, so its sum of digits is at most 27*d. But 27*d < 10^(d1) if d >= 3. Thus all terms for n >= 100 are 0.  Robert Israel, Mar 20 2016


LINKS



EXAMPLE

When n = 4, the digit sum of 4*k only equals 4 when k = 1 and k = 10; thus a(4) = 2.


MAPLE

f:= n > nops(select(t > convert(convert(n*t, base, 10), `+`)=n, [$0..n^2])):


PROG

(PARI) a(n) = sum(k=0, n^2, sumdigits(k*n)==n); \\ Michel Marcus, Feb 15 2016


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



