A268864 Number of integers of the form n*k whose digits sum up to n where 0 <= k <= n^2.

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

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^(d-1) <= 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^(d-1) if d >= 3. Thus all terms for n >= 100 are 0. - Robert Israel, Mar 20 2016

Links

Table of n, a(n) for n=0..81.

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])):
map(f, [$0..100]); # Robert Israel, Mar 20 2016

Prog

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

Crossrefs

Sequence in context: A210612 A266275 A288536 * A329956 A242703 A141456

Adjacent sequences: A268861 A268862 A268863 * A268865 A268866 A268867

Keyword

nonn,base

Author

Jordan G. Fischer, Feb 15 2016

Status

approved