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A309556
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Composite numbers m such that m divides Sum_{k=1..m-1} (lcm(1,2,...,(m-1)) / k)^2.
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0
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OFFSET
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1,1
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COMMENTS
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Composites m such that m | H_2(m-1) * lcm(1^2,2^2,...,(m-1)^2), where H_2(m) = 1/1^2 + 1/2^2 + ... + 1/m^2.
By Wolstenholme's theorem, if p > 3 is a prime, then p divides the numerator of H_2(p-1) and thus H_2(p-1) * lcm(1,2^2,...,(p-1)^2) == 0 (mod p). This sequence is formed by the pseudoprimes that are solutions of this congruence.
a(5) > 10^7 if it exists.
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LINKS
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MATHEMATICA
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s = 0; c = 1; n = 1; seq = {}; Do[s += 1/n^2; c = LCM[c, n^2]; n++; If[CompositeQ[n] && Divisible[s*c, n], AppendTo[seq, n]], {2 * 10^6}]; seq
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CROSSREFS
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KEYWORD
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nonn,bref,more
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AUTHOR
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STATUS
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approved
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