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A117360 Numbers m such that m and 2*m+1 have the same number of prime factors. 4

%I #10 Apr 30 2016 19:18:24

%S 2,3,4,5,10,11,23,25,29,34,38,40,41,46,52,53,55,57,76,77,83,89,91,93,

%T 106,113,118,123,129,130,131,133,143,145,159,161,169,171,172,173,177,

%U 179,185,191,201,203,205,206,212,213,218,220,226,233,235,238,239,251

%N Numbers m such that m and 2*m+1 have the same number of prime factors.

%C A001222(a(n)) = A001222(2*a(n)+1);

%C Sophie Germain primes are a subsequence, see A005384.

%H R. Zumkeller, <a href="/A117360/b117360.txt">Table of n, a(n) for n = 1..10000</a>

%e m=52=2*2*13, 2*52+1=105=3*5*7, therefore 52 is a term.

%t Select[Range[255], PrimeOmega[#] == PrimeOmega[2 # + 1] &] (* _Ivan Neretin_, Apr 30 2016 *)

%o (PARI) is(n)=bigomega(n)==bigomega(2*n+1) \\ _Charles R Greathouse IV_, Apr 30 2016

%Y Cf. A068406.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Mar 10 2006

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Last modified April 25 07:41 EDT 2024. Contains 371964 sequences. (Running on oeis4.)