BBC Russian

A335055

Odd infinitary abundant numbers whose infinitary abundancy is closer to 2 than that of any smaller odd infinitary abundant number.

945, 29835, 33345, 43065, 46035, 49875, 83265, 354585, 359205, 361515, 366135, 382305, 389235, 400785, 403095, 407715, 414645, 416955, 423885, 430815, 437745, 442365, 77967015, 132335385, 210124665, 719709375, 724239285, 1756753845, 9665740455, 10394173335

(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

Table of n, a(n) for n=1..30.

EXAMPLE

The infinitary abundancies of the first terms are 2.031..., 2.027..., 2.015..., 2.006..., 2.001..., ...

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, 10^5, 2}]; seq

CROSSREFS

Cf. A049417, A127666, A188263, A335052, A335053, A335054.

Sequence in context: A274756 A335053 A290034 * A133818 A334973 A334975

Adjacent sequences: A335052 A335053 A335054 * A335056 A335057 A335058

KEYWORD

nonn

AUTHOR

Amiram Eldar, May 21 2020

STATUS

approved