The On-Line Encyclopedia of Integer Sequences (OEIS)

A289995 revision #32

A289995

Numbers n with omega(n) <= 1 such that omega(n+1) = 1 or omega(n+2) = 1.

1, 2, 3, 4, 5, 7, 8, 9, 11, 16, 17, 23, 25, 27, 29, 31, 41, 47, 59, 71, 79, 81, 101, 107, 125, 127, 137, 149, 167, 179, 191, 197, 227, 239, 241, 256, 269, 281, 311, 347, 359, 419, 431, 461, 521, 569, 599, 617, 641, 659, 727, 809, 821, 827, 839, 857, 881, 1019, 1031, 1049

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OFFSET

1,2

COMMENTS

Every lesser of twin primes (A001359) is in the sequence. Every Fermat prime reduced by 1 and every Mersenne prime are in the sequence.

LINKS

Table of n, a(n) for n=1..60.

EXAMPLE

125 is in the sequence, since omega(125) = 1 and omega(125+2) = 1;

127 is in the sequence, since omega(127) = 1 and omega(127+1) = 1.

MATHEMATICA

Select[Range[3000], PrimeNu[#]<=1&&(PrimeNu[#+1]==1||PrimeNu[#+2]==1)&] (* Peter J. C. Moses, Sep 03 2017 *)