A162422 Numbers with at least 2 different numbers of digits among their prime factors.

22, 26, 33, 34, 38, 39, 44, 46, 51, 52, 55, 57, 58, 62, 65, 66, 68, 69, 74, 76, 77, 78, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 99, 102, 104, 106, 110, 111, 114, 115, 116, 117, 118, 119, 122, 123, 124, 129, 130, 132, 133, 134, 136, 138, 141, 142, 145, 146, 148, 152

Offset: 1

Author

Cino Hilliard, Jul 03 2009

Keywords

• base
• nonn

Comments

Complement of A162421. There are no prime numbers in this sequence.

These numbers can also be called factor rough numbers.

Basically, the number of digits of A020639(k) and of A006530(k) must differ to admit k into the sequence.

Examples

			1111 = 11*101 has factors with different digital lengths. Also it is the first occurrence that differs from A084891.
		

Crossrefs

Cf. A084891, A162457

Programs

PARI

factorrough(m,n) =
{
local(x,a,j,f,ln);
for(x=m,n, f=0; a = ifactor(x); for(j=2,length(a), ln=length(Str(a[j-1])); 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, definition shortened - R. J. Mathar, Sep 16 2009