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Search: id:A067513
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| A067513 |
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Number of divisors d of n such that d+1 is prime. |
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+0
8
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| 1, 2, 1, 3, 1, 3, 1, 3, 1, 3, 1, 5, 1, 2, 1, 4, 1, 4, 1, 4, 1, 3, 1, 5, 1, 2, 1, 4, 1, 5, 1, 4, 1, 2, 1, 7, 1, 2, 1, 5, 1, 4, 1, 4, 1, 3, 1, 6, 1, 3, 1, 4, 1, 4, 1, 4, 1, 3, 1, 8, 1, 2, 1, 4, 1, 5, 1, 3, 1, 4, 1, 8, 1, 2, 1, 3, 1, 4, 1, 6, 1, 3, 1, 7, 1, 2, 1, 5, 1, 6, 1, 4, 1, 2, 1, 7, 1, 2, 1, 5, 1, 4, 1
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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1, 2 and 4 are the only numbers such that for every divisor d, d+1 is a prime.
A067513(n) = 2 iff Bernoulli number B_{n} has denominator 6 (cf. A051222). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 13 2002
These and only these primes appear as prime divisors of any term of InvPhi[n] set if n is not empty, i.e. if n was from A002202. - Labos E. (labos(AT)ana.sote.hu), Jun 24 2002
a(n) <= A141197(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 06 2008]
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
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EXAMPLE
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a(12) = 5 as the divisors of 12 are 1, 2, 3, 4, 6 and 12 and the corresponding primes are 2,3,5,7 and 13. Only 3+1 = 4 is not a prime.
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MATHEMATICA
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a[n_] := Length[Select[Divisors[n]+1, PrimeQ]]
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CROSSREFS
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Even indexed terms gives A046886. Cf. A000005, A002202.
Sequence in context: A078079 A079728 A029244 this_sequence A116372 A029242 A029236
Adjacent sequences: A067510 A067511 A067512 this_sequence A067514 A067515 A067516
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 12 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Feb 12 2002
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