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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

%I #10 Jul 04 2023 14:48:01

%S 2,6,9,10,17,22,26,28,38,42,50,54,60,69,70,74,78,82,90,92,98,99,102,

%T 114,116,131,133,134,135,137,145,146,150,153,154,161,165,169,170,172,

%U 193,194,195,202,209,210,212,220,225,226,234,242,248,259,265,275,278,282

%N 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.

%C 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?

%C 2881008 has 14 1's in base 2 and 14 digits in its factorization. - _Harvey P. Dale_, Jul 04 2023

%H Harvey P. Dale, <a href="/A109600/b109600.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%Y Cf. A076649.

%K base,easy,nonn

%O 1,1

%A _Jason Earls_, Jul 30 2005

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Last modified May 30 04:46 EDT 2024. Contains 372958 sequences. (Running on oeis4.)