A091291 -id:A091291

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A091292

Numbers k such that the quotient (sigma(k) + sigma(k+1) + sigma(k+2))/sigma(3*k+3) is an integer.

+10
1

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

1,1

COMMENTS

Sum(sigma(j))/sigma(Sum(j)) for 3 terms summed up is integer.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..58

MATHEMATICA

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}]

PROG

(PARI) isok(n) = denominator((sigma(n) + sigma(n+1) + sigma(n+2))/sigma(3*n+3)) == 1; \\ Michel Marcus, Jul 29 2017

CROSSREFS

Cf. A000203, A091287, A091288, A091289, A091290, A091291, A091293.

KEYWORD

nonn

AUTHOR

Labos Elemer, Feb 17 2004

EXTENSIONS

a(15)-a(26) from Donovan Johnson, Feb 01 2009

a(27)-a(30) from Amiram Eldar, Mar 25 2024

STATUS

approved

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