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

A353502 Numbers with all prime indices and exponents > 2.

Original entry on oeis.org

1, 125, 343, 625, 1331, 2197, 2401, 3125, 4913, 6859, 12167, 14641, 15625, 16807, 24389, 28561, 29791, 42875, 50653, 68921, 78125, 79507, 83521, 103823, 117649, 130321, 148877, 161051, 166375, 205379, 214375, 226981, 274625, 279841, 300125, 300763, 357911
Offset: 1

Views

Author

Gus Wiseman, May 16 2022

Keywords

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Examples

			The initial terms together with their prime indices:
       1: {}
     125: {3,3,3}
     343: {4,4,4}
     625: {3,3,3,3}
    1331: {5,5,5}
    2197: {6,6,6}
    2401: {4,4,4,4}
    3125: {3,3,3,3,3}
    4913: {7,7,7}
    6859: {8,8,8}
   12167: {9,9,9}
   14641: {5,5,5,5}
   15625: {3,3,3,3,3,3}
   16807: {4,4,4,4,4}
   24389: {10,10,10}
   28561: {6,6,6,6}
   29791: {11,11,11}
   42875: {3,3,3,4,4,4}

Links

Crossrefs

The version for only parts is A007310, counted by A008483.
The version for <= 2 instead of > 2 is A018256, # of compositions A137200.
The version for only multiplicities is A036966, counted by A100405.
The version for indices and exponents prime (instead of > 2) is:
- listed by A346068
- counted by A351982
- only exponents: A056166, counted by A055923
- only parts: A076610, counted by A000607
The version for > 1 instead of > 2 is A062739, counted by A339222.
The version for compositions is counted by A353428, see A078012, A353400.
The partitions with these Heinz numbers are counted by A353501.
A000726 counts partitions with multiplicities <= 2, compositions A128695.
A001222 counts prime factors with multiplicity, distinct A001221.
A004250 counts partitions with some part > 2, compositions A008466.
A056239 adds up prime indices, row sums of A112798 and A296150.
A124010 gives prime signature, sorted A118914.
A295341 counts partitions with some multiplicity > 2, compositions A335464.
Cf. A000720, A003963, A065483, A114901, A181819, A353503, A353508.

Programs

  • Mathematica
    Select[Range[10000],#==1||!MemberQ[FactorInteger[#],{?(#<5&),}|{,?(#<3&)}]&]

Formula

Sum_{n>=1} 1/a(n) = Product_{p prime > 3} (1 + 1/(p^2*(p-1))) = (72/95)*A065483 = 1.0154153584... . - Amiram Eldar, May 28 2022
Previous Showing 11-20 of 24 results. Next

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

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