A155850 a(n) = smallest k > 1 such that k-1 and k+1 together have n prime divisors.

2, 4, 3, 5, 7, 15, 17, 31, 65, 129, 127, 449, 511, 2561, 1025, 7937, 12799, 20481, 8191, 28673, 65537, 131071, 458751, 360449, 966655, 524287, 4194303, 2097151, 29360129, 34865153, 67108865, 134217729, 33554431, 608174081, 268435457, 536870911, 4831838207

Offset: 1

Author

Klaus Brockhaus, Jan 28 2009, Jan 31 2009

Keywords

• nonn

Comments

Prime divisors are counted with multiplicity.

Similar to A155800, where k is restricted to primes.

Terms of the form 2^m-1 or 2^m+1 seem to occur frequently.

Examples

			Adjacent to 2 are the numbers 1 and 3 which together have one prime divisor, hence a(1) = 2. Adjacent to 3 are 2 and 4; together they have three prime divisors, hence a(3) = 3. Adjacent to 4 are the primes 3 and 5, each having one prime divisor; hence a(2) = 4.
For k = 129, k-1 = 128 = 2*2*2*2*2*2*2 and k+1 = 130 = 2*5*13 together have ten prime divisors. For all numbers k < 129 the adjacent numbers k-1 and k+1 together have fewer or more than ten (for 127 there are eleven) prime divisors, hence a(10) = 129.
		

Crossrefs

Cf. A001222 (number of prime divisors of n), A155800, A154704, A154598.

Programs

PARI

{for(n=2, 150000000, s=bigomega(n-1)+bigomega(n+1); if(v[s]==0, v[s]=n)); v}

Extensions

a(34)-a(37) from Donovan Johnson, Nov 02 2013