

A207006


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


1



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
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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



