A109600 Numbers n such that number of 1's in binary representation of n equals the number of digits required to write the prime factors of n.

2, 6, 9, 10, 17, 22, 26, 28, 38, 42, 50, 54, 60, 69, 70, 74, 78, 82, 90, 92, 98, 99, 102, 114, 116, 131, 133, 134, 135, 137, 145, 146, 150, 153, 154, 161, 165, 169, 170, 172, 193, 194, 195, 202, 209, 210, 212, 220, 225, 226, 234, 242, 248, 259, 265, 275, 278, 282

Offset: 1

Author

Jason Earls, Jul 30 2005

Keywords

• base
• easy
• nonn

Comments

708588 has 13 1's in base 2 and 13 digits in its factorization. What is the next term in this sequence with more 1's and digits?

2881008 has 14 1's in base 2 and 14 digits in its factorization. - Harvey P. Dale, Jul 04 2023

Examples

			54=110110 in base 2 and 54=2*3*3*3, hence 54 is in the sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A076649.

Programs

Mathematica

Select[Range[2,300],DigitCount[#,2,1]==Total[IntegerLength[#[[1]]]#[[2]]&/@ FactorInteger[ #]]&] (* Harvey P. Dale, Jul 04 2023 *)