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).
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
Keywords
Examples
A005117(5) = 6 = 2*3. a(5) = 1105 because 1105 is the smallest psp to both bases 2 and 3.
References
- Paulo Ribenboim, The New Book of Prime Number Records, New York: Springer-Verlag, p. 100, 1996.
Links
Programs
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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[ # ] &] -
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