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A187929
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Odd numbers k such that 1^((k-1)/2) + 2^((k-1)/2) + .... + (k-1)^((k-1)/2) == 0 (mod k).
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2
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1, 3, 5, 7, 11, 13, 15, 17, 19, 23, 27, 29, 31, 35, 37, 39, 41, 43, 47, 51, 53, 55, 59, 61, 63, 67, 71, 73, 75, 77, 79, 83, 85, 87, 89, 91, 95, 97, 99, 101, 103, 107, 109, 111, 113, 115, 119, 123, 125, 127, 131, 135, 137, 139, 143, 147, 149, 151, 155, 157, 159
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OFFSET
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1,2
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COMMENTS
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Asymptotic density is 0.379...
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LINKS
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José María Grau, Florian Luca and Antonio M. Oller-Marcén, On a variant of Giuga numbers, Acta Mathematica Sinica, English Series, Vol. 28 No. 4 (2012), pp 653-660; preprint, arXiv:1103.3428 [math.NT], 2011.
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MATHEMATICA
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gi[n_]:=Mod[Sum[PowerMod[j, (n-1)/2, n], {j, n-1}], n]; Select[ Range[1, 300, 2], gi[#]==0&]
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PROG
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(PARI) is(n)=my(e=(n-1)/2); sum(k=1, n-1, Mod(k, n)^e)==0;
select(is, vector(1000, i, 2*i-1)) \\ on older versions, switch the arguments
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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