A259312 -id:A259312 - cp's OEIS frontend

A307122 3-deficient numbers with increasing abundancy: Numbers k such that sigma(m)/m < sigma(k)/k < 3 for all numbers m < k such that sigma(m)/m < 3.

1, 2, 4, 6, 12, 24, 36, 48, 60, 168, 252, 300, 336, 630, 2268, 2310, 5472, 6804, 20412, 47424, 61236, 161304, 183708, 486096, 551124, 1215216, 1653372, 4081104, 4960116, 14880348, 44641044, 133923132, 401769396, 1205308188, 1631268870, 3615924564, 10847773692

Offset: 1

Amiram Eldar, Mar 26 2019

nonn

Analogous to A259312 with 3-deficient numbers instead of 3-abundant numbers.
Analogous to A228450 with ratio 3 instead of 2.
The values of sigma(a(n))/a(n) are 1, 1.5, 1.75, 2, 2.333..., 2.5, 2.527..., 2.583..., 2.8, ...

Cf. A071927, A023197, A228450, A259312.

sm=0; seq={}; Do[s=DivisorSigma[1,n]/n; If[s<3 && s>sm, sm=s; AppendTo[seq, n]], {n,1,100000}]; seq

A336671 Unitary barely 3-abundant: numbers m such that 3 < usigma(m)/m < usigma(k)/k for all numbers k < m, where usigma is the sum of unitary divisors function (A034448).

Original entry on oeis.org

30030, 39270, 43890, 46410, 51870, 62790, 67830, 79170, 82110, 91770, 103530, 161070, 166530, 709170, 718410, 723030, 732270, 764610, 778470, 801570, 806190, 815430, 829290, 833910, 847770, 861630, 875490, 884730, 155934030, 264670770, 1234205070, 1448478570

Offset: 1

Amiram Eldar, Jul 29 2020

nonn

The corresponding values of usigma(m)/m are 3.222..., 3.168...., 3.149..., 3.127..., 3.109..., ...

Amiram Eldar, Table of n, a(n) for n = 1..36

The unitary version of A259312.
Subsequence of A285615.
Cf. A034448, A034683, A302570, A336672.

usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); s = {}; rm = 4; Do[r = usigma[n]/n; If[r > 3 && r < rm, rm = r; AppendTo[s, n]], {n, 1, 10^5}]; s

cp's OEIS Frontend

A307122 3-deficient numbers with increasing abundancy: Numbers k such that sigma(m)/m < sigma(k)/k < 3 for all numbers m < k such that sigma(m)/m < 3.

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