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A155850 a(n) = smallest k > 1 such that k-1 and k+1 together have n prime divisors. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 5 10:38 EDT 2021. Contains 346466 sequences. (Running on oeis4.)