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A316348
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a(n) is the smallest k > 1 such that gcd(k, m^k - m) = 1 for all m = 2,...,n.
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1
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35, 35, 77, 77, 143, 143, 143, 143, 299, 299, 323, 323, 323, 323, 437, 437, 667, 667, 667, 667, 899, 899, 899, 899, 899, 899, 1457, 1457, 1739, 1739, 1739, 1739, 1739, 1739, 1763, 1763, 1763, 1763, 2021, 2021, 2491, 2491, 2491, 2491, 3127, 3127, 3127, 3127, 3127
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OFFSET
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2,1
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COMMENTS
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Conjecture: all the terms are in A121707.
GCD(n, a(n)) = 1. a(n) is odd.
Is a(n) squarefree?
a(n+1) >= a(n) by definition. (End)
It seems that a(prime(n+1)-1) > a(prime(n)-1) for n > 1. - Thomas Ordowski, Aug 13 2018
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LINKS
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FORMULA
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Conjecture: a(n) ~ n^2.
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PROG
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(PARI) isok(k, n)= {for (m=2, n, if (gcd(k, m^k - m) != 1, return (0)); ); return(1); }
a(n) = {my(k=2); while (! isok(k, n), k++); k; } \\ Michel Marcus, Aug 13 2018
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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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