A244397 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 have both the same distinct prime divisors.

22, 24, 28, 33, 39, 42, 44, 48, 55, 66, 77, 82, 84, 88, 93, 99, 111, 124, 164, 222, 248, 333, 444, 526, 548, 555, 666, 724, 777, 842, 888, 999, 1111, 1248, 1664, 2162, 2222, 2500, 2855, 3200, 3333, 3600, 3748, 4324, 4444, 4864, 5042, 5128, 5555, 5768, 5882

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 the prefix p = x(0)x(1)...x(q-1) and the suffix x(1)...x(q-1)x(q) have the same prime distinct divisors.

Examples

			3748 is in the sequence because 374 and 748 have the same prime divisors: {2,11,17}.
		

Crossrefs

Cf. A244394.

Programs

Maple

with(numtheory):
for n from 10 to 10000 do:
      x:=convert(n, base, 10):n1:=nops(x):
      s1 := n mod 10^ilog10(n):
      s2:=(n-irem(n,10))/10:
      x1:=factorset(s1):x2:=factorset(s2):
      if x1 = x2 and x1 <>{}
        then
        printf(`%d, `, n):
        else
      fi:
od: