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 1-8 of 8 results.

A259303 Numbers n such that there exists an x!=n that makes {x,x,n} an amicable multiset.

Original entry on oeis.org

1560, 7380, 20448, 20664, 22752, 23352, 25248, 26964, 35328, 51360, 100200, 104412, 108792, 135540, 156312, 192096, 232740, 252252, 278460, 310752, 362160, 401688, 492660, 543456, 548592, 588744, 659736, 732060, 767520, 826848, 998712, 999648, 1129440, 1129464
Offset: 1

Views

Author

Jeppe Stig Nielsen, Jun 23 2015

Keywords

Comments

We call the multiset {x,x,n} amicable iff sigma(x)=sigma(n)=x+x+n.
For the x values, see A259302.
If the condition x!=n were dropped, the terms from A005820 would also belong here.

Links

Crossrefs

Cf. A005820, A259307, A259302, A259304, A259305, A259306, A125490.

Programs

  • PARI
    isOK(n) = x=(sigma(n)-n)/2; x>0 && x!=n && denominator(x)==1 && sigma(x)==x+x+n;

A259302 Numbers n such that there exists an x!=n that makes {n,n,x} an amicable multiset.

Original entry on oeis.org

1740, 7776, 19260, 20640, 21384, 21924, 22428, 25830, 31440, 55968, 93024, 101010, 106140, 143910, 151164, 198792, 246510, 309582, 326196, 411138, 421596, 428256, 499464, 590112, 639288, 697158, 870552, 941094, 958716, 1060956, 1068210, 1087776, 1100640
Offset: 1

Views

Author

Jeppe Stig Nielsen, Jun 23 2015

Keywords

Comments

We call the multiset {n,n,x} amicable iff sigma(n)=sigma(x)=n+n+x.
For the x values, see A259303.
If the condition x!=n were dropped, the terms from A005820 would also belong here.

Links

Crossrefs

Cf. A005820, A259307, A259303, A259304, A259305, A259306, A125490.

Programs

  • PARI
    isOK(n) = x=sigma(n)-2*n; x>0 && x!=n && sigma(x)==n+n+x;

A259305 Numbers n such that there exists an x!=n that makes {x,x,x,n} an amicable multiset.

Original entry on oeis.org

756000, 1220940, 1437480, 1973160, 5019840, 9058140, 9703260, 11058480, 11641680, 13085280, 17089920, 18117000, 19370880, 21282912, 21628080, 25295760, 25585560, 26936640, 27763560, 28191240, 29104200, 29203020, 30450420, 32839560, 33279120, 33398820
Offset: 1

Views

Author

Jeppe Stig Nielsen, Jun 23 2015

Keywords

Comments

We call the multiset {x,x,x,n} amicable iff sigma(x)=sigma(n)=x+x+x+n.
For the x values, see A259304.
If the condition x!=n were dropped, the terms from A027687 would also belong here.

Links

Crossrefs

Cf. A027687, A259307, A259304, A259302, A259303, A259306, A036471.

Programs

  • PARI
    isOK(n) = x=(sigma(n)-n)/3; x>0&x!=n&denominator(x)==1&sigma(x)==3*x+n

A259306 Numbers n such that there exists an x!=n that makes {n,n,x,x} an amicable multiset.

Original entry on oeis.org

1441440, 1860768, 3205440, 3378240, 3423420, 3914820, 4029480, 4437720, 5738040, 6093360, 6807240, 7136640, 7239120, 7551360, 9402120, 10204740, 12270720, 12405120, 12942720, 13495680, 14627340, 14725620, 15233400, 17166240, 18097800, 19158048, 23023440
Offset: 1

Views

Author

Jeppe Stig Nielsen, Jun 23 2015

Keywords

Comments

We call the multiset {n,n,x,x} amicable iff sigma(n)=sigma(x)=n+n+x+x.
If the condition x!=n were dropped, the terms from A027687 would also belong here.

Links

Crossrefs

Cf. A027687, A259307, A259302, A259303, A259304, A259305, A036471.

Programs

  • PARI
    isOK(n) = x=(sigma(n)-2*n)/2; x>0 && x!=n && denominator(x)==1 && sigma(x)==n+n+x+x

A259307 Numbers that belong to at least one amicable multiset.

Original entry on oeis.org

1, 6, 28, 120, 220, 284, 496, 672, 1184, 1210, 1560, 1740, 1980, 2016, 2556, 2620, 2924, 5020, 5564, 6232, 6368, 7380, 7776, 8128, 9180, 9504, 10744, 10856, 11556, 12285, 14595, 17296, 18416, 19260, 20448, 20640, 20664, 21168, 21384, 21924, 22200, 22428, 22752
Offset: 1

Views

Author

Jeppe Stig Nielsen, Jun 23 2015

Keywords

Comments

Call a finite multiset {x_1, x_2, ..., x_k} of natural numbers (the x_i need not be distinct) an amicable multiset iff sigma(x_1)=sigma(x_2)=...=sigma(x_k)=x_1+x_2+...+x_k.
By definition, A255215 is a subset because a set can be regarded as a special multiset.
Also A007691 is a subset, since a k-perfect number corresponds to an amicable multiset in an obvious way. For example, since 120 is 3-perfect, the multiset {120, 120, 120} is amicable.
The first amicable multiset that belongs to neither A255215 nor A007691 is {1740, 1740, 1560}.

Links

Crossrefs

Cf. A255215, A007691, A259302, A259303, A259304, A259305, A259306.

Programs

  • PARI
    /* write amicable multisets */ sMax=10^7;sigmaVals=vector(sMax,x,[]);for(n=1,sMax,s=sigma(n);s<=sMax&sigmaVals[s]=concat(sigmaVals[s],[n]));(MultisetSum(numbers,desiredSum,track)=if(desiredSum<0,return);if(desiredSum==0,print(apply(x->numbers[x],track));return);for(i=if(track,track[#track],1),#numbers,MultisetSum(numbers,desiredSum-numbers[i],concat(track,[i]))));for(s=1,sMax,MultisetSum(sigmaVals[s],s,[]))

A273969 Numbers n such that there exists a pair x,y, where x

Original entry on oeis.org

702240, 817740, 1156680, 1159200, 1811040, 2450448, 2570400, 2784600, 3534300, 3912480, 4228560, 4546080, 4702320, 5682600, 6902280, 7280280, 7469280, 7706160, 8225280, 8316000, 8465184, 8522640, 8639400, 9025380, 9256800, 9282000, 9492120, 9828000
Offset: 1

Views

Author

John Cerkan, Jul 17 2016

Keywords

Comments

We call the multiset {x,y,n,n} amicable iff sigma(x) = sigma(y) = sigma(n) = x+y+n+n. For the x values, see A273970. For the y values, see A273971.
If the condition xA259306 would also belong here.

Examples

			sigma(695520) = sigma(803040) = sigma(702240) = 695520 + 803040 + 702240 + 702240.

Links

Crossrefs

Cf. A259302, A259303, A259304, A259305, A259306, A273970, A273971.

A273970 Numbers x such that there exist a pair y, n with x < y, x != n and y != n that makes {x,y,n,n} an amicable multiset.

Original entry on oeis.org

695520, 753480, 1113840, 1136520, 1784160, 2313360, 2898720, 3140280, 3865680, 3960600, 4272840, 4500720, 4626720, 6126120, 6167700, 7197960, 7442820, 7731360, 8177400, 8498700, 8784720, 8828820, 8920800, 8966160, 9124920, 9232860, 9664200, 9729720
Offset: 1

Views

Author

John Cerkan, Jul 17 2016

Keywords

Comments

We call the multiset {x,y,n,n} amicable iff sigma(x) = sigma(y) = sigma(n) = x+y+n+n. For the n values, see A273969. For the y values, see A273971.
If the condition xA259306 would also belong here.

Examples

			sigma(695520) = sigma(803040) = sigma(702240) = 695520 + 803040 + 702240 + 702240.

Links

Crossrefs

Cf. A259302, A259303, A259304, A259305, A259306, A273969, A273971.

A273971 Numbers y such that there exists a pair x, n, with x < y, x != n and y != n that makes {x,y,n,n} an amicable multiset.

Original entry on oeis.org

756000, 803040, 1267560, 1442448, 1851360, 2535120, 3209760, 3477240, 3926160, 3969840, 4413240, 4664880, 6094368, 6840540, 7617960, 7783020, 8027880, 8360352, 8586900, 9215640, 9559200, 9596520, 9697380, 9811620, 9815400, 9938160, 10063200, 10234224
Offset: 1

Views

Author

John Cerkan, Jul 17 2016

Keywords

Comments

We call the multiset {x,y,n,n} amicable iff sigma(x) = sigma(y) = sigma(n) = x+y+n+n. For the n values, see A273969. For the x values, see A273970.
If the condition xA259306 would also belong here.

Examples

			sigma(695520) = sigma(803040) = sigma(702240) = 695520 + 803040 + 702240 + 702240.

Links

Crossrefs

Cf. A259302, A259303, A259304, A259305, A259306, A273969, A273970.
Showing 1-8 of 8 results.

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