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.

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A018676 Divisors of 840.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

840 is a highly composite number: A002182(15)=840. - Reinhard Zumkeller, Jun 21 2010

Links

Crossrefs

Cf. A018253, A018256, A018261, A018266, A018293, A018321, A018350, A018412, A018609, A178877, A178878, A165412, A178858, A178859, A178860, A178861, A178862, A178863, A178864.

Programs

A178858 Divisors of 5040.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, 2520, 5040
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 21 2010

Keywords

Comments

5040 is a highly composite number: A002182(19)=5040;
the sequence is finite with A002183(19)=60 terms: a(60)=5040.

Links

Crossrefs

Cf. A018253, A018256, A018261, A018266, A018293, A018321, A018350, A018412, A018609, A018676, A178877, A178878, A165412, A178859, A178860, A178861, A178862, A178863, A178864.

Programs

A178859 Divisors of 7560.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 27, 28, 30, 35, 36, 40, 42, 45, 54, 56, 60, 63, 70, 72, 84, 90, 105, 108, 120, 126, 135, 140, 168, 180, 189, 210, 216, 252, 270, 280, 315, 360, 378, 420, 504, 540, 630, 756, 840, 945, 1080, 1260, 1512, 1890
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 21 2010

Keywords

Comments

7560 is a highly composite number: A002182(20)=7560.
The sequence is finite with A002183(20)=64 terms: a(64)=7560.
Its primorial factorization is 6^2 * 210 and its representing polynomial p(x) of degree 6 with x=2 is x^6 + 18x^5 + 118x^4 + 348x^3 + 457x^2 + 210x. - Carlos Eduardo Olivieri, May 02 2015

Links

Crossrefs

Cf. A018253, A018256, A018261, A018266, A018293, A018321, A018350, A018412, A018609, A018676, A178877, A178878, A165412, A178858, A178860, A178861, A178862, A178863, A178864.

Programs

A178860 Divisors of 10080.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 140, 144, 160, 168, 180, 210, 224, 240, 252, 280, 288, 315, 336, 360, 420, 480, 504, 560, 630, 672, 720, 840, 1008
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 21 2010

Keywords

Comments

10080 is a highly composite number: A002182(21)=10080.
The sequence is finite with A002183(21)=72 terms: a(72)=10080.

Links

Crossrefs

Cf. A018253, A018256, A018261, A018266, A018293, A018321, A018350, A018412, A018609, A018676, A178877, A178878, A165412, A178858, A178859, A178861, A178862, A178863, A178864.

Programs

A178861 Divisors of 15120.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 27, 28, 30, 35, 36, 40, 42, 45, 48, 54, 56, 60, 63, 70, 72, 80, 84, 90, 105, 108, 112, 120, 126, 135, 140, 144, 168, 180, 189, 210, 216, 240, 252, 270, 280, 315, 336, 360, 378, 420, 432, 504, 540, 560, 630
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 21 2010

Keywords

Comments

15120 is a highly composite number: A002182(22)=15120;
the sequence is finite with A002183(22)=80 terms: a(80)=15120.
15120 is the smallest number with 80 divisors; 18480 is the next smallest; there are 84 such numbers less than 100,000. - Harvey P. Dale, Dec 17 2013

Links

Crossrefs

Cf. A018253, A018256, A018261, A018266, A018293, A018321, A018350, A018412, A018609, A018676, A178877, A178878, A165412, A178858, A178859, A178860, A178862, A178863, A178864.

Programs

A178862 Divisors of 20160.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315, 320, 336, 360, 420, 448, 480, 504, 560, 576
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 21 2010

Keywords

Comments

20160 is a highly composite number: A002182(23)=20160.
The sequence is finite with A002183(23)=84 terms: a(84)=20160.

Links

Crossrefs

Cf. A018253, A018256, A018261, A018266, A018293, A018321, A018350, A018412, A018609, A018676, A178877, A178878, A165412, A178858, A178859, A178860, A178861, A178863, A178864.

Programs

A178863 Divisors of 25200.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 28, 30, 35, 36, 40, 42, 45, 48, 50, 56, 60, 63, 70, 72, 75, 80, 84, 90, 100, 105, 112, 120, 126, 140, 144, 150, 168, 175, 180, 200, 210, 225, 240, 252, 280, 300, 315, 336, 350, 360, 400, 420, 450, 504
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 21 2010

Keywords

Comments

25200 is a highly composite number: A002182(24)=25200;
the sequence is finite with A002183(24)=90 terms: a(90)=25200.

Links

Crossrefs

Cf. A018253, A018256, A018261, A018266, A018293, A018321, A018350, A018412, A018609, A018676, A178877, A178878, A165412, A178858, A178859, A178860, A178861, A178862, A178864.

Programs

A178877 Divisors of 1260.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 21 2010

Keywords

Comments

1260 is a highly composite number: A002182(16)=1260;
the sequence is finite with A002183(16)=36 terms: a(36)=1260.

Links

Crossrefs

Cf. A018253, A018256, A018261, A018266, A018293, A018321, A018350, A018412, A018609, A018676, A178878, A165412, A178858, A178859, A178860, A178861, A178862, A178863, A178864.

Programs

A178878 Divisors of 1680.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, 1680
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 21 2010

Keywords

Comments

1680 is a highly composite number: A002182(17)=1680;
the sequence is finite with A002183(17)=40 terms: a(40)=1680.

Links

Crossrefs

Cf. A018253, A018256, A018261, A018266, A018293, A018321, A018350, A018412, A018609, A018676, A178877, A165412, A178858, A178859, A178860, A178861, A178862, A178863, A178864.

Programs

A094783 Numbers k such that, for all m < k, d_i(k) <= d_i(m) for i=1 to Min(d(k),d(m)), where d_i(k) denotes the i-th smallest divisor of k.

Original entry on oeis.org

1, 2, 4, 6, 12, 24, 48, 60, 120, 240, 360, 1680, 2520, 5040, 10080, 15120, 25200, 27720, 55440, 110880, 166320, 277200, 720720, 1441440, 2162160, 3603600, 7207200, 10810800, 122522400, 183783600, 2327925600, 3491888400, 80313433200
Offset: 1

Views

Author

Matthew Vandermast, Jun 10 2004

Keywords

Comments

The function d(k) (A000005) is the number of divisors of k.
The defining criterion for this sequence is a sufficient, but not necessary, condition for membership in A095849.
Subsequence of A002182. - David Wasserman, Jun 28 2007
Why is 720 not in the sequence? The divisors of 360 begin 1,2,3,4,5,6,8,9,10,12,15,18 (A018412) and the divisors of 720 begin 1,2,3,4,5,6,8,9,10,12,15,16 (A018609). - J. Lowell, Aug 23 2007 [Answer from Don Reble, Sep 11 2007: 720 is precluded by 420. (1,2,3,4,5,6,7,10,12,14,15,20,21,...) (A018444).]
Conjecture: If k is in this sequence, then so is the smallest number with k divisors. (This conjecture is definitely false for A002182 (k=840) and A019505 (k=240).) - J. Lowell, Jan 24 2008

Examples

			As k increases, the positive integer k=6 sets or ties the existing records for smallest first, second and third-smallest divisors (1, 2 and 3), as well as for its fourth-smallest (6). Since no smaller integer has more than three divisors, 6 is a term of this sequence.

Links

Crossrefs

Cf. A123258.

Programs

  • PARI
    ge(va, vb) = {for(i=1, min(#va, #vb), if (va[i] > vb[i], return(0));); return(-1);}
isok(k) = {my(dk = divisors(k)); for (m=1, k-1, my(dm = divisors(m)); if (! ge(dk, dm), return(0));); return(1);} \\ Michel Marcus, Mar 16 2022

Extensions

More terms from David Wasserman, Jun 28 2007
Definition corrected by Ray Chandler, May 05 2008
Previous Showing 11-20 of 22 results. Next

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

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