cp's OEIS Frontend

A240520 Numbers that set a new integer record for the ratio between the product and the sum of their digits.

%I A240520 #14 Jul 23 2025 11:02:34
%S A240520 1,36,66,88,257,268,279,369,459,578,579,678,789,999,2589,2688,2799,
%T A240520 3699,3789,4599,4689,4789,5788,5889,7889,8888,18999,25889,26789,26888,
%U A240520 27788,28899,37899,38889,45999,46899,47799,47889,55899,56889,57789,58999,78999,257899
%N A240520 Numbers that set a new integer record for the ratio between the product and the sum of their digits.
%H A240520 Paolo P. Lava and Giovanni Resta, <a href="/A240520/b240520.txt">Table of n, a(n) for n = 1..1000</a> (first 100 terms from Paolo P. Lava)
%e A240520 For n = 2 we have 2 / 2 = 1.
%e A240520 For n = 36 we have 18 / 9 = 2.
%e A240520 For n = 66 we have 36 / 12 = 3.
%e A240520 For n = 88 we have 64 / 16 = 4.
%e A240520 Etc.
%p A240520 S:=proc(s) local j,w; w:=convert(s,base,10); sum(w[j],j=1..nops(w)); end:
%p A240520 U:=proc(s) local j,w; w:=convert(s,base,10); mul(w[j],j=1..nops(w)); end:
%p A240520 P:=proc(q) local a,n; a:=0;
%p A240520 for n from 2 to q do if type(U(n)/S(n),integer) then if U(n)/S(n)>a then
%p A240520 a:=U(n)/S(n); print(n); fi; fi; od; end: P(10^6);
%Y A240520 A038367.
%K A240520 nonn,easy,base
%O A240520 1,2
%A A240520 _Paolo P. Lava_, Apr 07 2014