A162421 Numbers whose prime factors all have the same number of digits.

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 27, 28, 29, 30, 31, 32, 35, 36, 37, 40, 41, 42, 43, 45, 47, 48, 49, 50, 53, 54, 56, 59, 60, 61, 63, 64, 67, 70, 71, 72, 73, 75, 79, 80, 81, 83, 84, 89, 90, 96, 97, 98, 100, 101, 103, 105, 107

Offset: 1

Author

Cino Hilliard, Jul 03 2009

Keywords

• base
• nonn

Comments

The prime numbers A000040 are a subset of this sequence.

A number k>1 is in this sequence, if the count of base-10 digits of all entries in the k-th row of A027746 (=its prime factors) is the same.

Examples

			16 = 2*2*2*2 and the digital length = 1 for all factors. So 16 is in the sequence. 22=2*11 is not in the sequence because the digital length of 11 is not the same as the digital length of 2.
		

Crossrefs

Cf. A162422

Programs

PARI

factorsmooth(n) =
{
local(x,a,j,f,ln);
for(x=2,n, f=0; a = ifactor(x); ln=length(Str(a[1])); for(j=2,length(a), if(length(Str(a[j]))!=ln,f=1;break);); if(!f,print1(x","));)
};

Formula

{k >1: A055642(A020639(k)) = A055642(A006530(k)) }. - R. J. Mathar, Sep 16 2009

Extensions

Offset set to 1 - R. J. Mathar, Sep 16 2009