A353539 Starts of runs of 3 consecutive numbers whose abundancy index is larger than Pi^2/6.

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

Offset: 1

Author

Amiram Eldar, Apr 25 2022

Keywords

• nonn

Comments

The least odd term is a(64391) = 8110375.

Examples

			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... .
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A013661.

Subsequence of A353537 and A353538.

Subsequences: A096536, A353540, A353541.

Programs

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]

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