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

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, 55, 56, 63, 72, 74, 75, 80, 85, 86, 91, 92, 93, 94, 96, 98, 102, 104, 106, 115, 116, 117, 122, 127, 133, 134, 141, 142, 143, 144, 145, 146, 153, 158, 159, 160, 162

Offset: 1

Author

Michel Lagneau, Feb 14 2012

Keywords

• nonn

Comments

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).

Examples

			12 is in the sequence because omega(12) = 2, omega(12 + 2) = omega(14) = 2.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221, A207005, A005384 , A175760, A175759.

Programs

Mathematica

Select[Range[5*10^2],PrimeNu[#]==PrimeNu[#+PrimeNu[#]]&]

PARI

is(n)=my(o=omega(n));o==omega(n+o) \\ Charles R Greathouse IV, Feb 14 2012