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.

655, 5848, 176594, 25820986, 1394797593315

Offset: 1

Author

Paolo P. Lava, Jan 03 2017

Keywords

• nonn
• base
• more

Comments

The ratios for a(1)-a(5) are 1, 2, 3, 4, and 7, respectively. a(6) > 10^13. - Giovanni Resta, Jan 05 2017

Examples

			655 = concat(6,55) = concat(65,5) and (6*55 + 65*5)/655 = 1;
5848 = concat(5,848) = concat(58,48) = concat(584,8) and (5*848 + 58*48 + 584*8)/5848 = 2; etc.
		

Crossrefs

Cf. A280446, A280447.

Programs

Maple

P:=proc(q) local a,j,k,n; j:=0; for n from 1 to q do a:=0;
for k from 1 to ilog10(n) do a:=a+(n mod 10^k)*trunc(n/10^k); od;
if type(a/n,integer) then if a/n>j then j:=a/n; print(n); fi; fi; od; end: P(10^9);

Extensions

a(5) from Giovanni Resta, Jan 05 2017