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 A353539 Starts of runs of 3 consecutive numbers whose abundancy index is larger than Pi^2/6. 6
 188, 230, 284, 374, 404, 434, 440, 494, 824, 854, 944, 1034, 1070, 1274, 1448, 1664, 1826, 1910, 1988, 2114, 2330, 2534, 2708, 2924, 3014, 3374, 3548, 3590, 3674, 3716, 3794, 3968, 4184, 4388, 4598, 4634, 4850, 5024, 5048, 5228, 5444, 5474, 5564, 5642, 5864, 5894 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The least odd term is a(64391) = 8110375. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE 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... . MATHEMATICA 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] PROG (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 CROSSREFS Cf. A000203, A013661. Subsequence of A353537 and A353538. Subsequences: A096536, A353540, A353541. Sequence in context: A015986 A065212 A044998 * A243077 A186397 A260836 Adjacent sequences: A353536 A353537 A353538 * A353540 A353541 A353542 KEYWORD nonn AUTHOR Amiram Eldar, Apr 25 2022 STATUS approved

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Last modified August 2 21:27 EDT 2024. Contains 374875 sequences. (Running on oeis4.)