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%I A037478 #15 Jan 15 2020 15:52:48
%S A037478 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,
%T A037478 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,
%U A037478 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
%N A037478 Number of positive solutions to "numbers that are n times sum of their digits".
%C A037478 It appears that the largest terms occur when n=1 mod 9 and moderately large terms when n=4 or 7 mod 9.
%H A037478 Giovanni Resta, <a href="/A037478/b037478.txt">Table of n, a(n) for n = 1..10000</a>
%e A037478 a(13)=3 since the only three solutions are 117=9*13, 156=12*13 and 195=15*13.
%p A037478 read("transforms"):
%p A037478 A037478 := proc(n)
%p A037478     local a,x,k;
%p A037478     a := 0 ;
%p A037478     for k from 1 do
%p A037478         x := n*k ;
%p A037478         if digsum(x)*n = x then
%p A037478             a := a+1 ;
%p A037478         end if;
%p A037478         # may stop if x/digsum(x)>n, so if x/#digits(x) > 9*n
%p A037478         if x/A055642(x) > 9*n then
%p A037478             break;
%p A037478         end if;
%p A037478     end do:
%p A037478     a ;
%p A037478 end proc:
%p A037478 seq(A037478(n),n=1..101) ; # _R. J. Mathar_, May 11 2016
%Y A037478 Cf. A003634, A003635, A005349, A052489, A052490, A057147, A058913.
%K A037478 nonn,base
%O A037478 1,1
%A A037478 _Henry Bottomley_, Sep 12 2000

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