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 1-2 of 2 results.

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

Original entry on oeis.org

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

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Author

Jaroslav Krizek, Jan 22 2012

Keywords

Comments

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

Examples

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

Links

Crossrefs

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

A291458 Numbers n having a proper divisor d such that sigma(n) - k*d = k*n. Case k = 4.

Original entry on oeis.org

27720, 60480, 65520, 90720, 98280, 105840, 115920, 120120, 120960, 128520, 131040, 143640, 151200, 163800, 180180, 191520, 205920, 207900, 211680, 218400, 229320, 235620, 241920, 249480, 264600, 272160, 289800, 292320, 312480, 332640, 360360, 372960, 393120, 414960
Offset: 1

Views

Author

Paolo P. Lava, Aug 24 2017

Keywords

Comments

Case k=2 are the admirable numbers (A111592).
Subset of A023198, A068404, A204831, A230608.

Examples

			One of the proper divisors of 27720 is 360 and sigma(27720) - 4*360 = 112320 - 1440 = 110880 = 4*27720.
One of the proper divisors of 115920 is 144 and sigma(115920) - 4*144 = 464256 - 576 = 463680 = 4*115920.

Links

Crossrefs

Cf. A000203, A023198, A068404, A111592, A204831, A230608, A291457, A291459.

Programs

  • Maple
    with(numtheory): P:=proc(q,h) local a,k,n; for n from 1 to q do a:=sort([op(divisors(n))]);
for k from 1 to nops(a)-1 do if sigma(n)-h*a[k]=h*n then print(n); break; fi; od; od; end: P(10^9,4);
  • Mathematica
    With[{k = 4}, Select[Range[5 * 10^5], Function[n, AnyTrue[Most@ Divisors@ n, DivisorSigma[1, n] - k # == k n &]]]] (* Michael De Vlieger, Aug 24 2017 *)
(* or *)
k=4; Select[Range[5*^5], (t = DivisorSigma[1, #]/k - #; #>t>0 && IntegerQ[t] && Mod[#, t] == 0) &] (* much faster, Giovanni Resta, Aug 25 2017 *)
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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