A336252 Infinitary barely deficient numbers: infinitary deficient numbers whose infinitary abundancy is closer to 2 than that of any smaller infinitary deficient number.

1, 2, 8, 84, 110, 128, 1155, 3680, 6490, 8200, 8648, 12008, 18632, 32768, 724000, 1495688, 2095208, 3214090, 3477608, 3660008, 5076008, 12026888, 16102808, 26347688, 29322008, 33653888, 73995392, 615206030, 815634435, 2147483648, 42783299288, 80999455688

Offset: 1

Author

Amiram Eldar, Jul 14 2020

Keywords

• nonn

Comments

The infinitary abundancy of a number k is isigma(k)/k, where isigma is the sum of infinitary divisors of k (A049417).

The corresponding values of the infinitary abundancy are 1, 1.5, 1.875, 1.904..., 1.963..., ...

Examples

			8 is a term since it is infinitary deficient (A129657), and isigma(8)/8 = 15/8 is higher than isigma(k)/k for all the infinitary deficient numbers k < 8.
		

Crossrefs

Cf. A049417, A129657, A335054.

Similar sequences: A228450, A262228, A302572, A307122, A336253.

Programs

Mathematica

fun[p_, e_] := Module[{b = IntegerDigits[e, 2]}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ fun @@@ FactorInteger[n]; seq = {}; r = 0; Do[s = isigma[n]/n; If[s < 2 && s > r, AppendTo[seq, n]; r = s], {n, 1, 10^6}]; seq