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Search: id:A110874
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| A110874 |
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Number of prime factors with multiplicity of 2 + (n^(n+1)). |
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+0
1
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| 1, 2, 1, 5, 2, 2, 4, 5, 2, 5, 4, 4, 5, 3, 1, 4, 5, 3, 4, 6, 3, 8, 4, 5, 4, 4, 2, 6, 3, 6, 5, 5, 5, 6, 6, 8, 6, 6, 4, 5, 4
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Compared with A110676, number of prime factors with multiplicity of 2 + (n^(n+1)), this seems to have an unlimited number of primes (n = 1, 3, 15, ...) and semiprimes (n = 2, 5, 6, 9, 27, ...). Of course, n even gives n | a(n).
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FORMULA
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a(1) = 1. For n>1, a(n) = A001222(1 + A110567(n)) = A001222(2 + A007778(n)) = A001222(2 + (n^(n+1))).
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EXAMPLE
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a(1) = 1 because 2 + 1^2 = 3 is prime (one prime factor).
a(2) = 2 because 2 + 2^3 = 10 = 2 * 5 is semiprime (two prime factors).
a(3) = 1 because 2 + 3^4 = 83 is prime.
a(4) = 5 because 2 + 4^5 = 1026 = 2 * 3^3 * 19 has five prime factors (3 has multiplicity of 3).
a(5) = 2 because 2 + 5^6 = 15627 = 3 * 5209 is semiprime (two prime factors).
a(6) = 2 because 2 + 6^7 = 279938 = 2 * 139969 is semiprime (two prime factors).
a(15) = 1 because 2 + 15^16 = 6568408355712890627 is prime. What is the next prime?
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CROSSREFS
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Cf. A001222, A007778, A110567, A110676.
Sequence in context: A137151 A048494 A047848 this_sequence A010253 A065274 A136262
Adjacent sequences: A110871 A110872 A110873 this_sequence A110875 A110876 A110877
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Sep 18 2005
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