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A353939
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Smallest b > 1 such that b^(p-1) == 1 (mod p^6) for p = prime(n).
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8
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65, 728, 1068, 34967, 284995, 861642, 390112, 333257, 2818778, 42137700, 8078311, 33518159, 92331463, 21583010, 138173066, 8202731, 390421192, 1006953931, 77622331, 270657300, 5915704483, 522911165, 2507851273, 1329885769, 2789067613, 3987072867, 7938255646
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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a[n_] := Module[{p = Prime[n], b = 2}, While[PowerMod[b, p - 1, p^6] != 1, b++]; b]; Array[a, 9] (* Amiram Eldar, May 12 2022 *)
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PROG
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(PARI) a(n) = my(p=prime(n)); for(b=2, oo, if(Mod(b, p^6)^(p-1)==1, return(b)))
(Python)
from sympy import prime
from sympy.ntheory.residue_ntheory import nthroot_mod
def A353939(n): return 2**6+1 if n == 1 else int(nthroot_mod(1, (p:= prime(n))-1, p**6, True)[1]) # Chai Wah Wu, May 17 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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