

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.


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



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



KEYWORD

base,easy,nonn


AUTHOR



STATUS

approved



