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.

A139718 A number n is included if |k - n/k| divides n for at least one divisor k of n.

Original entry on oeis.org

2, 6, 8, 12, 18, 20, 24, 30, 32, 36, 42, 48, 50, 54, 56, 60, 72, 80, 90, 96, 98, 108, 110, 120, 128, 132, 140, 144, 150, 156, 162, 168, 180, 182, 192, 200, 210, 216, 224, 240, 242, 252, 270, 272, 288, 294, 300, 306, 320, 324, 336, 338, 342, 350, 360, 378, 380
Offset: 1

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Author

Leroy Quet, May 01 2008

Keywords

Comments

All terms are even. All positive integers of the form n(n+1) are included.

Examples

			36 is included because 3 is a divisor of 36 and |3 - 36/3| = 9 divides 36.

Links

Crossrefs

Cf. A139719.

Programs

  • Mathematica
    For[n = 1; s = {}, n <= 1000, n++,
  For[i = 1, i <= Length[Divisors[n]], i++, k = Divisors[n][[i]];
    If[Abs[k-n/k]>0&&Mod[n, Abs[k-n/k]]==0,s=Union[s,{n}];Break[]]]];s (* Alexis Olson (AlexisOlson(AT)gmail.com), Nov 14 2008 *)
odkQ[n_]:=Module[{d=Divisors[n],nz},nz=#-n/#&/@d; MemberQ[Divisible[ n,Abs[Select[nz,#!=0&]]],True]]; Select[Range[400],odkQ] (* Harvey P. Dale, May 06 2012 *)

Extensions

More terms from Alexis Olson (AlexisOlson(AT)gmail.com), Nov 14 2008

A163188 Numbers of the form n = r*s = (r+s)*t with gcd(r+s,t) = 1.

Original entry on oeis.org

4, 18, 48, 100, 150, 180, 294, 448, 490, 588, 648, 900, 960, 1134, 1210, 1584, 1620, 2028, 2100, 2178, 2548, 2904, 3150, 3388, 3630, 3718, 3840, 4624, 5040, 5070, 5508, 5850, 6084, 6468, 6498, 6760, 7098, 7600, 8670, 8820, 9900, 9984, 10164, 11638
Offset: 1

Views

Author

Hagen von Eitzen, Jul 22 2009

Keywords

Comments

Also numbers of the form n = u*v*(u+v)^2 with gcd(u,v) = 1. The connection to the definition is given by r = u*(u+v), s = v*(u+v), t = u*v, resp. u = gcd(r,t), v = gcd(s,t).
Also "primitive" members of A139719: With k as in the definition of A139719, we additionally require that gcd(k+n/k, n/(k+n/k)) = 1.
100 has a non-primitive solution with k=10, resp. (r,s,t) = (10,10,5), resp. (u,v) = (5,5). It is included because there is also the primitive solution k=5, resp. (r,s,t) = (5,20,4), resp. (u,v) = (1,4).
8820 has two primitive solutions: k=21, resp. (r,s,t) = (21,420,20), resp. (u,v) = (1,20) and k=70, resp. (r,s,t) = (70,126,45), resp. (u,v) = (5,9).

Examples

			4 is in the sequence because 4 = 2*2 = (2+2)*1, gcd(2+2,1)=1.
18 is in the sequence because 18 = 3*6 = (3+6)*2, gcd(3+6,2)=1.
48 is in the sequence because 48 = 4*12 = (4+12)*3, gcd(4+12,3)=1.
16 = 4*4 = (4+4)*2 is not sufficient to make 16 a member of the sequence because gcd(4+4,2)=2.

Crossrefs

Cf. A139719.

Programs

  • PARI
    L=10000;v=[];for(r=1,L^(1/3),for(s=1,r,if(gcd(r,s)==1, n=r*s*(r+s)^2; if(n>L,break);if(n==8820,print([r,s]));v=concat(v,n))));vecsort(eval(Set(v)))
Showing 1-2 of 2 results.

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

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