cp's OEIS Frontend

A244394 Consider a number n with m decimal digits, m>1. The sequence lists the numbers n such that the prefix of length m-1 and the suffix of length m-1 both have the same sum of divisors.

%I A244394 #21 Jul 02 2014 17:10:27
%S A244394 11,22,33,44,55,66,77,88,99,111,222,333,335,444,534,551,555,579,589,
%T A244394 666,682,777,888,954,956,999,1102,1111,2138,2204,2222,2246,2649,3190,
%U A244394 3333,4354,4408,4428,4444,5332,5376,5555,5644,5925,6294,6666,6933,7480,7528
%N A244394 Consider a number n with m decimal digits, m>1. The sequence lists the numbers n such that the prefix of length m-1 and the suffix of length m-1 both have the same sum of divisors.
%C A244394 Let x(0)x(1)... x(q-1)x(q) denote the decimal expansion of a number n. The sequence lists the numbers n such that sigma(p) = sigma(s) where p is the prefix x(0)x(1)... x(q-1) and s is the suffix x(1)... x(q-1)x(q).
%e A244394 5376 is in the sequence because sigma(537) = sigma(376) = 720.
%p A244394 with(numtheory):
%p A244394 for n from 10 to 10000 do:
%p A244394       x:=convert(n, base, 10):n1:=nops(x):
%p A244394       s1:=sum('x[i]*10^(i-1) ', 'i'=1..n1-1):
%p A244394       s2:=(n-irem(n,10))/10:
%p A244394       x1:=sigma(s1):x2:=sigma(s2):
%p A244394       if x1 = x2
%p A244394         then
%p A244394         printf(`%d, `, n):
%p A244394         else
%p A244394       fi:
%p A244394 od:
%Y A244394 Cf. A244282, A244283.
%K A244394 nonn,base
%O A244394 1,1
%A A244394 _Michel Lagneau_, Jun 27 2014