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

1,2

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).

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A353848 A330722 A220969 * A171781 A329395 A065294

Adjacent sequences: A207003 A207004 A207005 * A207007 A207008 A207009

Keyword

nonn

Author

Michel Lagneau, Feb 14 2012

Status

approved