cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A204829 Numbers with abundancy 2 <= a < 3.

Original entry on oeis.org

6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234, 246, 252
Offset: 1

Views

Author

Jaroslav Krizek, Jan 22 2012

Keywords

Comments

Numbers m such that 2 <= sigma(m) / m < 3.
Supersequence of A000396 (perfect numbers).

Examples

			Number 70 is in sequence because sigma(70) / 70 = 144 / 70, which is between 2 and 3.

Links

Crossrefs

Cf. A204828 (abundant numbers with abundancy 3 <= a < 4).

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

Views

Author

Jaroslav Krizek, Nov 29 2013

Keywords

Comments

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

Examples

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

Links

Crossrefs

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).

Programs

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

Extensions

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

A291457 Numbers n having a proper divisor d such that sigma(n) - k*d = k*n. Case k = 3.

Original entry on oeis.org

180, 240, 360, 420, 480, 540, 600, 660, 780, 840, 1080, 1320, 1560, 1890, 1920, 2016, 2040, 2184, 2280, 2352, 2376, 2688, 2760, 2856, 3000, 3192, 3360, 3480, 3720, 3744, 4284, 4320, 4440, 4680, 4704, 4896, 4920, 5160, 5292, 5640, 5796, 6048, 6360, 6552, 7080, 7128
Offset: 1

Views

Author

Paolo P. Lava, Aug 24 2017

Keywords

Comments

Case k=2 are the admirable numbers (A111592).
Subset of A023197, A068403, A068545, A204828, A204830.

Examples

			One of the proper divisors of 1080 is 120 and sigma(1080) - 3*120 = 3600 - 360 = 3240 = 3*1080.
One of the proper divisors of 17850 is 6 and sigma(17850) - 3*6 = 53568 - 18 = 53550 = 3*17850.

Links

Crossrefs

Cf. A000203, A023197, A068403, A068545, A111592, A204828, A204830, A291458, A291459.

Programs

  • Maple
    with(numtheory): P:=proc(q,h) local a,b,c,k; c:=0; a:=sort([op(divisors(q))]); for k from 1 to nops(a)-1 do if sigma(q)-h*a[k]=h*q then c:=1; break; fi; od; if c=1 then q; fi; end: seq(P(i,3),i=1..7200);
  • Mathematica
    k=3; Select[Range[7128], (t = DivisorSigma[1, #]/k - #; # > t > 0 && IntegerQ[t] && Mod[#, t] == 0) &] (* Giovanni Resta, Aug 25 2017 *)
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.