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

1,2

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..., ...

Links

Table of n, a(n) for n=1..32.

Example

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.

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

Crossrefs

Cf. A049417, A129657, A335054.

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

Sequence in context: A013175 A120820 A295600 * A276488 A295764 A261683

Adjacent sequences: A336249 A336250 A336251 * A336253 A336254 A336255

Keyword

nonn

Author

Amiram Eldar, Jul 14 2020

Status

approved