A282706 Smallest prime factor of A020549(n) = (n!)^2 + 1.
2, 2, 5, 37, 577, 14401, 13, 101, 17, 131681894401, 13168189440001, 1593350922240001, 101, 38775788043632640001, 29, 1344169, 149, 9049, 37, 710341, 41, 61, 337, 509, 384956219213331276939737002152967117209600000001, 941
Offset: 0
Keywords
References
- T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 147.
Links
- Hugo Pfoertner, Table of n, a(n) for n = 0..74
- Apoloniusz Tyszka, On ZFC-formulae phi(x) for which we know a non-negative integer n such that max({x, element of N, phi(x)}) <= n if the set {x, element of N, phi(x)} is finite, 2019.
- Apoloniusz Tyszka, Sławomir Kurpaska, Open problems that concern computable sets X, subset of N, and cannot be formally stated as they refer to current knowledge about X, (2020).
- Andrew Walker, Table of factors of (n!)^2+1.
Programs
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Magma
[2] cat [Min(PrimeFactors(Factorial(n)^2 + 1)):n in[1..25]]; // Vincenzo Librandi, Feb 28 2017
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Maple
f:= proc(n) local a; a:= min(map(proc(t) if t[1]::integer then t[1] fi end proc, ifactors((n!)^2+1,easy)[2])); if a = infinity then a:= traperror(timelimit(60, min(map(t -> t[1], ifactors((n!)^2+1)[2])))); fi; a end proc: map(f, [$0..36]); # Robert Israel, Mar 08 2017
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Mathematica
Join[{2}, Array[FactorInteger[(#!)^2 + 1][[1, 1]]&, {25}]] (* Vincenzo Librandi, Feb 28 2017 *)
Extensions
More terms from Vincenzo Librandi, Feb 28 2017
Comments