A204829 -id:A204829 - cp's OEIS frontend

A204828 Numbers n with abundancy 3 <= sigma(n)/n < 4.

120, 180, 240, 360, 420, 480, 504, 540, 600, 660, 672, 720, 780, 840, 900, 960, 1008, 1080, 1200, 1260, 1320, 1344, 1440, 1512, 1560, 1584, 1620, 1680, 1800, 1848, 1872, 1890, 1920, 1980, 2016, 2040, 2100, 2160, 2184, 2280, 2340, 2352, 2376, 2400, 2520, 2640

Offset: 1

Jaroslav Krizek, Jan 22 2012

nonn

A subsequence of A023197 (numbers n such that sigma(n) >= 3n) which is in turn a subsequence of the abundant numbers A005101, i.e., numbers n with sigma(n)/n > 2.
Differs from A023197 from a(565) on: The first term of A023197 which is not in this sequence is A023197(565) = 27720 = A023198(1) = A023199(4), the least number with abundancy >= 4.
Numbers with abundancy sigma(n)/n < 2 are called deficient and listed in A005100. Numbers with sigma(n)/n in the interval [2,3) are listed in A204829. Numbers with sigma(n)/n in the interval [4,5) are listed in A230608. - M. F. Hasler, Dec 05 2013

			Number 180 is in the sequence because sigma(180)/180 = 546/180 = 3.0333...

Jaroslav Krizek, Table of n, a(n) for n = 1..3000
Eric Weisstein's World of Mathematics, Abundancy
Eric Weisstein's World of Mathematics, Abundant Number

Cf. A204829 (abundant numbers with abundancy 2 <= a < 3).

A230608 Numbers with abundancy 4 <= sigma(n)/n < 5.

Original entry on oeis.org

27720, 30240, 32760, 50400, 55440, 60480, 65520, 75600, 83160, 85680, 90720, 95760, 98280, 100800, 105840, 110880, 115920, 120120, 120960, 128520, 131040, 138600, 141120, 143640, 151200, 163800, 166320, 171360, 176400, 180180, 181440, 184800, 191520, 194040

Offset: 1

Jaroslav Krizek, Nov 29 2013

nonn

A subsequence of A023198 (numbers with abundancy >= 4). It differs from A023198 from a(31093) on: The term A023198(31093) = 122522400 = A023199(5) = A215264(1) is not in this sequence. It excludes all terms of A215264, but also the 5-perfect numbers A046060, which are neither in this sequence nor in A215264. [Corrected by M. F. Hasler, Dec 05 2013]
A108775(a(n)) = 4.
There are 31092 terms less than 122522399. - T. D. Noe, Dec 04 2013

			27720 is in sequence because sigma(27720) / 27720 = 112320 / 27720 = 4.0519....

Jaroslav Krizek, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Abundancy
Eric Weisstein's World of Mathematics, Abundant Number

Cf. A000203, A023198, A023199, A108775.
Cf. A005100 (deficient numbers with abundancy 1 <= a < 2),
Cf. A204829 (numbers with abundancy 2 <= a < 3),
Cf. A204828 (abundant numbers with abundancy 3 <= a < 4).
Cf. A215264 (abundant numbers with abundancy > 5).

Select[Range[200000], 4 <= DivisorSigma[1, #]/# < 5 &] (* T. D. Noe, Dec 04 2013 *)

Corrected and edited by M. F. Hasler, Dec 05 2013

cp's OEIS Frontend

A204828 Numbers n with abundancy 3 <= sigma(n)/n < 4.

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