cp's OEIS Frontend

A280445 Consider a number k and all the possible concatenations of the form k = concat(a,b), with a>0. Take the sum of the products of all the pairs a and b, j = Sum{a*b}. Sequence lists the numbers for which j/k is an integer and produce a new record.

%I A280445 #12 Jan 05 2017 05:49:06
%S A280445 655,5848,176594,25820986,1394797593315
%N A280445 Consider a number k and all the possible concatenations of the form k = concat(a,b), with a>0. Take the sum of the products of all the pairs a and b, j = Sum{a*b}. Sequence lists the numbers for which j/k is an integer and produce a new record.
%C A280445 The ratios for a(1)-a(5) are 1, 2, 3, 4, and 7, respectively. a(6) > 10^13. - _Giovanni Resta_, Jan 05 2017
%e A280445 655 = concat(6,55) = concat(65,5) and (6*55 + 65*5)/655 = 1;
%e A280445 5848 = concat(5,848) = concat(58,48) = concat(584,8) and (5*848 + 58*48 + 584*8)/5848 = 2; etc.
%p A280445 P:=proc(q) local a,j,k,n; j:=0; for n from 1 to q do a:=0;
%p A280445 for k from 1 to ilog10(n) do a:=a+(n mod 10^k)*trunc(n/10^k); od;
%p A280445 if type(a/n,integer) then if a/n>j then j:=a/n; print(n); fi; fi; od; end: P(10^9);
%Y A280445 Cf. A280446, A280447.
%K A280445 nonn,base,more
%O A280445 1,1
%A A280445 _Paolo P. Lava_, Jan 03 2017
%E A280445 a(5) from _Giovanni Resta_, Jan 05 2017