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

Author

Henry Bottomley, Sep 12 2000

Keywords

• nonn
• base

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

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