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

1,1

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).

Links

Table of n, a(n) for n=1..49.

Example

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

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:

Crossrefs

Cf. A244282, A244283.

Sequence in context: A071273 A377948 A226467 * A299792 A115853 A050785

Adjacent sequences: A244391 A244392 A244393 * A244395 A244396 A244397

Keyword

nonn,base

Author

Michel Lagneau, Jun 27 2014

Status

approved