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A242441
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Numbers n such that there are no integer k < sqrt(n) and prime p < n with k^2*p == 1 (mod n).
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4
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1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 18, 20, 21, 24, 28, 30, 32, 39, 40, 48, 50, 56, 60, 63, 70, 72, 80, 88, 102, 110, 112, 120, 126, 156, 168, 204, 213, 220, 232, 240, 252, 272, 273, 280, 312, 372, 378, 408, 520, 527, 546, 760, 765, 780, 813, 840, 968, 1320, 1715, 1848
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OFFSET
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1,2
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COMMENTS
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Conjecture: The sequence only has 61 terms as listed.
We have checked this extension of the conjecture in A242425 for n up to 10^7.
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LINKS
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EXAMPLE
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a(5) = 5 since none of 1^2*2 = 2, 1^2*3 = 3, 2^2*2 = 8 and 2^2*3 = 12 is congruent to 1 modulo 5.
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MATHEMATICA
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r[k_, n_]:=r[k, n]=PowerMod[k^2, -1, n]
m=0; Do[Do[If[GCD[k, n]==1&&PrimeQ[r[k, n]], Goto[aa]], {k, 1, Sqrt[n-1]}]; m=m+1; Print[m, " ", n]; Label[aa]; Continue, {n, 1, 2000}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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