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A335054 Infinitary barely abundant numbers: infinitary abundant numbers whose infinitary abundancy is closer to 2 than that of any smaller infinitary abundant number. 4
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 (list; graph; refs; listen; history; text; internal format)
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 * A125639 A076496 A125640

Adjacent sequences:  A335051 A335052 A335053 * A335055 A335056 A335057

KEYWORD

nonn

AUTHOR

Amiram Eldar, May 21 2020

STATUS

approved

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Last modified July 28 19:33 EDT 2021. Contains 346335 sequences. (Running on oeis4.)