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%I #11 Apr 26 2022 04:45:41
%S 188,230,284,374,404,434,440,494,824,854,944,1034,1070,1274,1448,1664,
%T 1826,1910,1988,2114,2330,2534,2708,2924,3014,3374,3548,3590,3674,
%U 3716,3794,3968,4184,4388,4598,4634,4850,5024,5048,5228,5444,5474,5564,5642,5864,5894
%N Starts of runs of 3 consecutive numbers whose abundancy index is larger than Pi^2/6.
%C The least odd term is a(64391) = 8110375.
%H Amiram Eldar, <a href="/A353539/b353539.txt">Table of n, a(n) for n = 1..10000</a>
%e 188 is a term since sigma(188)/188 = 336/188 = 1.787..., sigma(189)/189 = 320/189 = 1.693... and sigma(190)/190 = 360/190 = 1.894... are all larger than Pi^2/6 = 1.644... .
%t q[n_] := DivisorSigma[-1, n] > Pi^2/6; seq[count_, nConsec_] := Module[{tri = q /@ Range[nConsec], s = {}, c = 0, k = nConsec + 1}, While[c < count, If[And @@ tri, c++; AppendTo[s, k - nConsec]]; tri = Join[Rest[tri], {q[k]}]; k++]; s]; seq[46, 3]
%o (PARI) isok(k) = ((sigma(k)/k) > Pi^2/6) && ((sigma(k+1)/(k+1)) > Pi^2/6) && ((sigma(k+2)/(k+2)) > Pi^2/6); \\ _Michel Marcus_, Apr 25 2022
%Y Cf. A000203, A013661.
%Y Subsequence of A353537 and A353538.
%Y Subsequences: A096536, A353540, A353541.
%K nonn
%O 1,1
%A _Amiram Eldar_, Apr 25 2022
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