A268582 Sphenic numbers having identical digits.

66, 222, 555, 777, 2222, 3333, 5555, 7777, 22222, 33333, 55555, 77777, 2222222, 3333333, 5555555, 7777777, 22222222222, 33333333333, 55555555555, 77777777777, 1111111111111, 22222222222222222, 33333333333333333, 55555555555555555, 77777777777777777, 6666666666666666666

Offset: 1

Author

Michel Lagneau, Feb 07 2016

Keywords

• nonn
• base

Comments

Subsequence of A007304 (sphenic numbers: products of 3 distinct primes).

a(1)= A087331(4).

Examples

			222 is in the sequence because 222 = 2*3*37, product of 3 distinct primes.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..89

Crossrefs

Cf. A007304, A046053, A087331, A095370, A196104.

Programs

Maple

with(numtheory):
for n from 1 to 23 do:
  for b from 1 to 9 do:
    x:=(((10^n)- 1)/9)*b:y:=factorset(x):n1:=nops(y):
     if bigomega(x)=3 and n1=3
      then
      printf(`%d, `,x):
      else
     fi:
   od:
od:

Mathematica

Select[Flatten@ Map[Map[Function[k, FromDigits@ Table[k, {#}]], Range[1, 9]] &, Range@ 20], Length@ # == 3 && Times @@ Last /@ # == 1 &@ FactorInteger@ # &] (* Michael De Vlieger, Feb 07 2016 *)