A207005 Numbers k such that omega(k) = omega(k - omega(k)) where omega(k) is the number of distinct primes dividing k.

1, 3, 4, 5, 8, 9, 12, 14, 17, 20, 22, 24, 26, 28, 32, 35, 36, 38, 40, 46, 48, 50, 52, 54, 56, 57, 58, 65, 74, 76, 77, 82, 87, 88, 93, 94, 95, 96, 98, 100, 105, 106, 108, 117, 118, 119, 124, 128, 135, 136, 143, 144, 145, 146, 147, 148, 155, 160, 161, 162, 164

Offset: 1

Author

Michel Lagneau, Feb 14 2012

Keywords

• nonn

Comments

omega is the function in A001221. If there are infinitely many primes p such that p and 2p-1 are primes (see A005382), then this sequence is infinite. Proof: the numbers of the form 4p are in a subsequence if p and 2p-1 are both prime, 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(10) = 2.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A001221, A005382.

Programs

Mathematica

Select[Range[10^4],PrimeNu[#]==PrimeNu[#-PrimeNu[#]]&]