A037478 Number of positive solutions to "numbers that are n times sum of their digits".

9, 1, 1, 4, 1, 1, 4, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 11, 1, 1, 3, 1, 1, 3, 2, 2, 12, 1, 1, 3, 1, 1, 4, 1, 2, 15, 2, 1, 4, 1, 1, 3, 1, 1, 13, 2, 2, 3, 1, 1, 4, 1, 1, 13, 1, 1, 2, 1, 1, 3, 0, 0, 7, 0, 1, 4, 1, 1, 4, 1, 1, 8, 1, 0, 3, 1, 1, 4, 1, 1, 10, 1, 0, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 0, 1, 3, 1, 1, 9, 1

Offset

1,1

Comments

It appears that the largest terms occur when n=1 mod 9 and moderately large terms when n=4 or 7 mod 9.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Example

a(13)=3 since the only three solutions are 117=9*13, 156=12*13 and 195=15*13.

Maple

read("transforms"):
A037478 := proc(n)
    local a, x, k;
    a := 0 ;
    for k from 1 do
        x := n*k ;
        if digsum(x)*n = x then
            a := a+1 ;
        end if;
        # may stop if x/digsum(x)>n, so if x/#digits(x) > 9*n
        if x/A055642(x) > 9*n then
            break;
        end if;
    end do:
    a ;
end proc:
seq(A037478(n), n=1..101) ; # R. J. Mathar, May 11 2016

Crossrefs

Cf. A003634, A003635, A005349, A052489, A052490, A057147, A058913.

Sequence in context: A200128 A225537 A109012 * A198551 A010162 A228409

Adjacent sequences: A037475 A037476 A037477 * A037479 A037480 A037481

Keyword

nonn,base

Author

Henry Bottomley, Sep 12 2000

Status

approved