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A316940
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Smallest "anti-Carmichael pseudoprime" to base n.
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3
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35, 7957, 16531, 1247, 17767, 35, 817, 2501, 697, 4141, 2257, 143, 9577, 2257, 4187, 1247, 3991, 221, 7957, 2059, 55, 161, 1027, 115, 403, 475, 247, 4553, 35, 247, 6289, 697, 1853, 35, 1247, 35, 589, 221, 95, 533, 35, 559, 77, 215, 253, 235, 221, 329, 247, 119
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OFFSET
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1,1
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COMMENTS
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a(n) is the smallest k such that n^(k-1) == 1 (mod k) and p-1 does not divide k-1 for every prime p dividing k.
All listed terms are semiprime and squarefree, except a(26) = 475 = 5^2*19.
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LINKS
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MATHEMATICA
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Table[Block[{k = 2}, While[Nand[PowerMod[n, k - 1, k] == 1, AllTrue[FactorInteger[k][[All, 1]] - 1, Mod[k - 1, #] != 0 &]], k++]; k], {n, 50}] (* Michael De Vlieger, Jul 20 2018 *)
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PROG
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(PARI) isok(k, n) = {if (!isprime(k) && Mod(n, k)^(k-1) == 1, f = factor(k)[, 1]; for (j=1, #f~, if (!((k-1) % (f[j]-1)), return (0)); ); return (1); ); return (0); }
a(n) = {my(k=2); while(!isok(k, n), k++); k; } \\ Michel Marcus, Jul 17 2018
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CROSSREFS
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Cf. A121707 (probably "anti-Carmichael numbers": n such that p-1 does not divide n-1 for every prime p dividing n).
Cf. A316907 ("anti-Carmichael pseudoprimes" to base 2).
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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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