cp's OEIS Frontend

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

%I A162421 #6 Oct 01 2013 21:35:30
%S A162421 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,
%T A162421 29,30,31,32,35,36,37,40,41,42,43,45,47,48,49,50,53,54,56,59,60,61,63,
%U A162421 64,67,70,71,72,73,75,79,80,81,83,84,89,90,96,97,98,100,101,103,105,107
%N A162421 Numbers whose prime factors all have the same number of digits.
%C A162421 The prime numbers A000040 are a subset of this sequence.
%C A162421 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.
%F A162421 {k >1: A055642(A020639(k)) = A055642(A006530(k)) }. - R. J. Mathar, Sep 16 2009
%e A162421 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.
%o A162421 (PARI) factorsmooth(n) =
%o A162421 {
%o A162421 local(x,a,j,f,ln);
%o A162421 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","));)
%o A162421 };
%Y A162421 Cf. A162422
%K A162421 base,nonn
%O A162421 1,1
%A A162421 _Cino Hilliard_, Jul 03 2009
%E A162421 Offset set to 1 - _R. J. Mathar_, Sep 16 2009