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%I #41 Jan 26 2024 11:29:12
%S 9,341,91,217,1105,25,561,15,21,561,1541,45,45,703,645,33,561,35,1729,
%T 49,703,1729,561,45,561,1891,105,1105,77,341,65,91,65,1729,1105,341,
%U 87,91,561,561,1105,85,91,561,105,111,561,703,2465,91,561,105,781,561,91
%N 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).
%D Paulo Ribenboim, The New Book of Prime Number Records, New York: Springer-Verlag, p. 100, 1996.
%H Amiram Eldar, <a href="/A098650/b098650.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>
%e A005117(5) = 6 = 2*3. a(5) = 1105 because 1105 is the smallest psp to both bases 2 and 3.
%t 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[ # ] &]
%o (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
%Y Cf. A005117, A007535, A098651 (indices of records), A098652 (records).
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Sep 18 2004