A335054 Infinitary barely abundant numbers: infinitary abundant numbers whose infinitary abundancy is closer to 2 than that of any smaller infinitary abundant number.

24, 30, 40, 54, 56, 70, 88, 104, 642, 654, 678, 726, 762, 786, 822, 834, 894, 906, 942, 978, 1002, 1014, 1038, 1074, 1086, 1146, 1158, 1182, 1194, 1266, 1338, 1362, 1374, 1398, 1434, 1446, 1506, 1536, 1542, 1578, 1596, 2406, 2454, 2514, 2526, 2586, 2598, 2634

Offset

1,1

Comments

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

Links

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

Example

The infinitary abundancies of the first terms are 2.5, 2.4, 2.25, 2.222..., 2.142..., 2.057..., ...

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 = 3; Do[s = isigma[n]/n; If[s > 2 && s < r, AppendTo[seq, n]; r = s], {n, 1, 3000}]; seq

Crossrefs

The infinitary version of A071927.

Cf. A049417, A129656, A302570, A302571.

Sequence in context: A111398 A030626 A302571 * A348604 A347063 A371920

Adjacent sequences: A335051 A335052 A335053 * A335055 A335056 A335057

Keyword

nonn

Author

Amiram Eldar, May 21 2020

Status

approved