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

Author

Amiram Eldar, May 21 2020

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

The infinitary version of A071927.

Cf. A049417, A129656, A302570, A302571.

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