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

1,1

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

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A076649.

Sequence in context: A243373 A085304 A015843 * A370802 A370810 A071814

Adjacent sequences: A109597 A109598 A109599 * A109601 A109602 A109603

Keyword

base,easy,nonn

Author

Jason Earls, Jul 30 2005

Status

approved