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Search: id:A098650
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| A098650 |
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Smallest odd pseudoprime k > b to bases p_i, i.e. the smallest composite number k > b such that p_i^(k-1)-1 is divisible by k, p_i are the prime factors of b and b is square-free. |
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+0
5
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| 9, 341, 91, 217, 1105, 25, 561, 15, 21, 561, 1541, 45, 45, 703, 645, 33, 561, 35, 1729, 49, 703, 1729, 561, 45, 561, 1891, 105, 1105, 77, 341, 65, 91, 65, 1729, 1105, 341, 87, 91, 561, 561, 1105, 85, 91, 561, 105, 111, 561, 703, 2465, 91, 561, 105, 781, 561, 91
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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Ribenboim, P., The New Book of Prime Number Records. New York: Springer-Verlag, p. 100, 1996.
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EXAMPLE
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a(n) is the A005117(n). A005117(5)=6=2*3. a(5)=1105 because 1105 is the
smallest psp to both the bases 2&3.
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MATHEMATICA
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(* first do *) Needs["NumberTheory`NumberTheoryFunctions`"] (* then *) PrimeFactors[ n_ ] := Flatten[ Table[ # [[ 1 ]], {1} ] & /@ FactorInteger[ n ]]; f[n_] := Block[{k = n + 1}, If[ EvenQ[k], k++ ]; While[ PrimeQ[k] || Union[ PowerMod[ PrimeFactors[n], k - 1, k]] != {1}, k += 2]; k]; f /@ Select[ Range[90], SquareFreeQ[ # ] &]
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CROSSREFS
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Cf. A007535, A005117, records in A098651 & A098652.
Sequence in context: A152553 A090087 A090085 this_sequence A098652 A110695 A157589
Adjacent sequences: A098647 A098648 A098649 this_sequence A098651 A098652 A098653
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 18 2004
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