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A091292
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Numbers k such that the quotient (sigma(k) + sigma(k+1) + sigma(k+2))/sigma(3*k+3) is an integer.
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1
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424, 2134, 20154, 23954, 27344, 27584, 37414, 45154, 74874, 89654, 503810, 1327292, 1910174, 8976614, 13954744, 17386316, 20920074, 22436224, 22937784, 23253068, 29705192, 70524530, 78617972, 81607504, 85815924, 94163306, 107161784, 114195964, 115314294, 149806904
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OFFSET
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1,1
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COMMENTS
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Sum(sigma(j))/sigma(Sum(j)) for 3 terms summed up is integer.
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LINKS
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MATHEMATICA
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sg[n_] := DivisorSigma[1, n]; g[x_, k_] := Apply[Plus, Table[sg[x + j], {j, 0, k - 1}]] / sg[Apply[Plus, Table[x + j, {j, 0, k - 1}]]]; Do[s = g[n, 3]; If[IntegerQ[s], Print[n]], {n, 1, 10000000}]
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PROG
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(PARI) isok(n) = denominator((sigma(n) + sigma(n+1) + sigma(n+2))/sigma(3*n+3)) == 1; \\ Michel Marcus, Jul 29 2017
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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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