A090096 Least n-pseudoprime which is a power of a prime number; smallest prime-power pseudoprime to base n.
4, 1194649, 121, 1194649, 4, 4377277921, 25, 9, 4, 9, 5041, 7252249, 4, 841, 848615161, 1194649, 4, 25, 9, 78961, 4, 169, 169, 25, 4, 9, 121, 9, 4, 49, 49, 25, 4, 2129445719544546771481, 9, 4377277921, 4, 289, 64625521, 121, 4, 529, 25, 9, 4, 9
Offset: 1
Examples
n=2: -1+2^(1092*1094) = K*1093*1093 = K*1194649; n=4k+1: a(4k+1)=4; for a(k)=9 see A090097; a(k)=25 see A090098. Some large values after a(46): a(52)=219521; a(56)=418609; a(58)=17161; a(59)=7711729; a(83)=23726641; a(84)=26569; a(86)=4656561121; a(87)=3996001; a(92)=528529; a(95)=4566769; a(96)=11881. Hard bases below 100 are 47, 66, 72, 88, 90.
Programs
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Mathematica
t=list-of-true-p-powers-generated-independently lf[x_] := Length[FactorInteger[x]] base=6;Do[s=Mod[ -1+base^(Part[t, n]-1), Part[t, n]]; If[Equal[s, 0], Print[Part[t, n]]], {n, 1, Length[t]}]
Formula
a(n) = A039951(n)^2.
Extensions
More terms from Michel Marcus, Aug 30 2019