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A249275
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a(n) is the smallest b > 1 such that p = prime(n) satisfies b^(p-1) == 1 (mod p^3).
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11
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9, 26, 57, 18, 124, 239, 158, 333, 42, 1215, 513, 691, 1172, 3038, 295, 1468, 2511, 15458, 3859, 6372, 923, 1523, 5436, 1148, 412, 4943, 4432, 5573, 476, 68, 21304, 30422, 6021, 8881, 33731, 25667, 3868, 3170, 17987, 26626, 43588, 7296, 14628, 22076, 138057
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OFFSET
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1,1
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COMMENTS
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LINKS
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MATHEMATICA
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Array[Block[{b = 2}, While[PowerMod[b, # - 1, #^3] != 1, b++]; b] &@ Prime@ # &, 45] (* Michael De Vlieger, Nov 25 2018 *)
dpa[n_]:=Module[{p=Prime[n], a=9}, While[PowerMod[a, p - 1, p^3]!=1, a++]; a]; Array[dpa, 50] (* Vincenzo Librandi, Nov 30 2018 *)
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PROG
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(PARI) a(n) = my(p=prime(n)); for(b=2, oo, if(Mod(b, p^3)^(p-1)==1, return(b)))
(Python)
from sympy import prime
def a(n):
b, p = 2, prime(n)
p3 = p**3
while pow(b, p-1, p3) != 1: b += 1
return b
(Python)
from sympy import prime
from sympy.ntheory.residue_ntheory import nthroot_mod
def A249275(n): return 2**3+1 if n == 1 else int(nthroot_mod(1, (p:= prime(n))-1, p**3, 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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