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A098650
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, where b is the n-th squarefree number, A005117(n).
5
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
OFFSET
1,1
REFERENCES
Paulo Ribenboim, The New Book of Prime Number Records, New York: Springer-Verlag, p. 100, 1996.
EXAMPLE
A005117(5) = 6 = 2*3. a(5) = 1105 because 1105 is the smallest psp to both bases 2 and 3.
MATHEMATICA
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[ # ] &]
PROG
(PARI) lista(nn) = my(f, k); for(b=1, nn, if(issquarefree(b), f=factor(b)[, 1]; k=b+1+b%2; while(isprime(k) || sum(i=1, #f, Mod(f[i], k)^(k-1)==1)<#f, k+=2); print1(k, ", "))); \\ Jinyuan Wang, Jul 24 2021
CROSSREFS
Cf. A005117, A007535, A098651 (indices of records), A098652 (records).
Sequence in context: A152553 A090087 A090085 * A354689 A098652 A110695
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Sep 18 2004
STATUS
approved