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

1,1

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.

Links

Table of n, a(n) for n=1..70.

Formula

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

Example

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.

Prog

(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", ")); )
};

Crossrefs

Cf. A162422

Sequence in context: A274399 A276181 A171829 * A275164 A076499 A092629

Adjacent sequences: A162418 A162419 A162420 * A162422 A162423 A162424

Keyword

base,nonn

Author

Cino Hilliard, Jul 03 2009

Extensions

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

Status

approved