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 1-3 of 3 results.

A054481 Highest common factor of successive highly composite numbers (1), A002182.

Original entry on oeis.org

1, 2, 2, 6, 12, 12, 12, 12, 60, 60, 60, 120, 360, 120, 420, 420, 840, 2520, 2520, 2520, 5040, 5040, 5040, 2520, 2520, 5040, 5040, 27720, 27720, 55440, 55440, 55440, 55440, 166320, 55440, 110880, 55440, 360360, 360360
Offset: 2

Views

Author

Henry Bottomley, Mar 31 2000

Keywords

Comments

Not the same as the first differences of A002182. The latter are given by A262501, which differs from this sequence for the first time at n=25, where A262501(25) = 17640, while here the 25th term a(26) is 2520. The sequences differ next time at positions n = 52, 53, 54, 64, 67, 82, 83, 84, 85, 86, 87, 88, 90, 91, 96, 100, 106, ... (when one-based indexing as in A262501 is used). - Antti Karttunen, Sep 24 2015

Examples

			a(7)=12 because A002182(7)=36, A002182(6)=24 and GCD(36,24)=12.

Links

Crossrefs

Cf. A002182, A054482, A054483, A262501.

Formula

a(n) = GCD(A002182(n-1), A002182(n)) = A002182(n)/A054483(n) = A002182(n-1)/A054482(n).

Extensions

Erroneous comment (wrong interpretation) removed by Antti Karttunen, Sep 25 2015

A054483 Numerator of lowest terms fraction from division of a highly composite number (1) by its predecessor.

Original entry on oeis.org

2, 2, 3, 2, 2, 3, 4, 5, 2, 3, 4, 3, 2, 7, 3, 4, 3, 2, 3, 4, 3, 4, 5, 11, 18, 10, 11, 3, 4, 3, 4, 5, 6, 3, 10, 6, 13, 3, 4, 3, 4, 5, 6, 3, 10, 6, 5, 4, 6, 5, 3, 17, 20, 17, 6, 3, 10, 6, 5, 4, 6, 5, 3, 19, 20, 3, 19, 3, 20, 19, 6, 5, 4, 6, 5, 3, 4, 3, 4, 3, 7, 46, 105, 23, 28, 46, 105, 23, 3, 28, 23, 3
Offset: 2

Views

Author

Henry Bottomley, Mar 31 2000

Keywords

Comments

Successive fractions are 2/1,2/1,3/2,2/1,2/1,3/2,4/3,5/4,2/1,3/2,4/3,3/2,2/1 a(n) is frequently A054482(n)+1, though not for example for n=26.

Examples

			a(7)=3 since A002182(7)=36, A002182(6)=24 and 36/24=3/2 in lowest terms.

Links

Crossrefs

Cf. A002182, A054482.

Programs

  • Mathematica
    s = Import["https://oeis.org/A002182/b002182.txt", "Data"][[All, -1]]; Array[Numerator[s[[# + 1]]/s[[#]]] &, 120] (* Michael De Vlieger, Oct 11 2023 *)

Formula

a(n) = A002182(n)/A054481(n).

Extensions

More terms from Jud McCranie, Jun 11 2005

A053878 Difference between numerator and denominator of lowest terms fraction from division of a highly composite number (1) by its predecessor.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 13, 2, 5, 11, 13, 2, 1, 5, 2, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1
Offset: 2

Views

Author

Henry Bottomley, Mar 31 2000

Keywords

Comments

Successive fractions are 2/1, 2/1, 3/2, 2/1, 2/1, 3/2, 4/3, 5/4, 2/1, 3/2, 4/3, 3/2, 2/1.
This sequence is not multiplicative.

Examples

			a(7)=1 since A002182(7)=36, A002182(6)=24, 36/24=3/2 in lowest terms and 3-2=1.

Crossrefs

Cf. A002182.

Formula

a(n) = A054483(n)-A054482(n) =(A002182(n)-A002182(n-1))/A054481(n).

Extensions

More terms from Jud McCranie, Jun 09 2005
Showing 1-3 of 3 results.

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