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URL: https://oeis.org/A155850

⇱ A155850 - OEIS

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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
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.
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
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Jan 28 2009, Jan 31 2009
EXTENSIONS
a(34)-a(37) from Donovan Johnson, Nov 02 2013
STATUS
approved