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A336252 Infinitary barely deficient numbers: infinitary deficient numbers whose infinitary abundancy is closer to 2 than that of any smaller infinitary deficient number. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 2 21:48 EDT 2022. Contains 355029 sequences. (Running on oeis4.)