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.

11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 335, 444, 534, 551, 555, 579, 589, 666, 682, 777, 888, 954, 956, 999, 1102, 1111, 2138, 2204, 2222, 2246, 2649, 3190, 3333, 4354, 4408, 4428, 4444, 5332, 5376, 5555, 5644, 5925, 6294, 6666, 6933, 7480, 7528

Offset: 1

Author

Michel Lagneau, Jun 27 2014

Keywords

• nonn
• base

Comments

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).

Examples

			5376 is in the sequence because sigma(537) = sigma(376) = 720.
		

Crossrefs

Cf. A244282, A244283.

Programs

Maple

with(numtheory):
for n from 10 to 10000 do:
      x:=convert(n, base, 10):n1:=nops(x):
      s1:=sum('x[i]*10^(i-1) ', 'i'=1..n1-1):
      s2:=(n-irem(n,10))/10:
      x1:=sigma(s1):x2:=sigma(s2):
      if x1 = x2
        then
        printf(`%d, `, n):
        else
      fi:
od: