cp's OEIS Frontend

A207006 Numbers n such that omega(n) = omega(n + omega(n)) where omega(n) is the number of distinct primes dividing n.

%I A207006 #9 May 13 2013 01:54:21
%S A207006 1,2,3,4,7,8,10,12,16,18,20,22,24,26,31,33,34,36,38,44,46,48,50,52,54,
%T A207006 55,56,63,72,74,75,80,85,86,91,92,93,94,96,98,102,104,106,115,116,117,
%U A207006 122,127,133,134,141,142,143,144,145,146,153,158,159,160,162
%N A207006 Numbers n such that omega(n) = omega(n + omega(n)) where omega(n) is the number of distinct primes dividing n.
%C A207006 omega is the function in A001221. If there are infinitely many Sophie Germain primes (see A005384), then this sequence is infinite. Proof : the numbers of the form 4p are in a subsequence if p and 2p+1 are both primes, because from the property that omega(4p) = 2 and omega (p(2p+1)) =  2, if n = 4p then omega (n+omega(n)) = omega (4p + 2) = omega (2(2p+1)) = 2 = omega (n).
%H A207006 Charles R Greathouse IV, <a href="/A207006/b207006.txt">Table of n, a(n) for n = 1..10000</a>
%e A207006 12 is in the sequence because omega(12) = 2, omega(12 + 2) = omega(14) = 2.
%t A207006 Select[Range[5*10^2],PrimeNu[#]==PrimeNu[#+PrimeNu[#]]&]
%o A207006 (PARI) is(n)=my(o=omega(n));o==omega(n+o) \\ _Charles R Greathouse IV_, Feb 14 2012
%Y A207006 Cf. A001221, A207005, A005384 , A175760, A175759.
%K A207006 nonn
%O A207006 1,2
%A A207006 _Michel Lagneau_, Feb 14 2012