A091292 - OEIS

%I #31 Jan 12 2025 11:05:41

%S 424,2134,20154,23954,27344,27584,37414,45154,74874,89654,503810,

%T 1327292,1910174,8976614,13954744,17386316,20920074,22436224,22937784,

%U 23253068,29705192,70524530,78617972,81607504,85815924,94163306,107161784,114195964,115314294,149806904

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

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

%H Amiram Eldar, <a href="/A091292/b091292.txt">Table of n, a(n) for n = 1..58</a>

%t 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}]

%t Select[Range[600000],IntegerQ[(DivisorSigma[1,#]+DivisorSigma[1,#+1]+DivisorSigma[1,#+2])/DivisorSigma[1,3#+3]]&] (* The program generates the first 11 terms of the sequence. *) (* _Harvey P. Dale_, Dec 23 2024 *)

%o (PARI) isok(n) = denominator((sigma(n) + sigma(n+1) + sigma(n+2))/sigma(3*n+3)) == 1; \\ _Michel Marcus_, Jul 29 2017

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

%K nonn

%O 1,1

%A _Labos Elemer_, Feb 17 2004

%E a(15)-a(26) from _Donovan Johnson_, Feb 01 2009

%E a(27)-a(30) from _Amiram Eldar_, Mar 25 2024