|
| |
|
|
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
|
| |
|
|
