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

1,1

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.

Links

Table of n, a(n) for n=1..37.

Example

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.

Prog

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

Crossrefs

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

Sequence in context: A082006 A277375 A232798 * A134464 A104472 A316964

Adjacent sequences: A155847 A155848 A155849 * A155851 A155852 A155853

Keyword

nonn

Author

Klaus Brockhaus, Jan 28 2009, Jan 31 2009

Extensions

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

Status

approved