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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A070705 LCM of first n prime powers modulo next prime power.

Original entry on oeis.org

2, 2, 2, 4, 4, 3, 1, 4, 8, 5, 14, 15, 5, 18, 1, 20, 16, 2, 15, 15, 8, 21, 29, 21, 16, 32, 29, 23, 22, 30, 54, 71, 37, 7, 37, 43, 45, 30, 36, 77, 100, 72, 64, 7, 56, 33, 42, 54, 132, 18, 90, 156, 91, 29, 86, 149, 139, 111, 112, 96, 62, 5, 204, 103, 41, 197, 81, 218, 128, 238, 58
Offset: 1

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Author

Lekraj Beedassy, May 15 2002

Keywords

Examples

			The case n=7 implies a(7) = A051451(7) (mod A000961(8)) = lcm(2,3,4,5,7,8,9) (mod 11) = 2520 (mod 11) = 1.

Crossrefs

Cf. A051451, A000961.

Formula

a(n) = A051451(n) (mod A000961(n+1)) = A051126(A051451(n), A000961(n-1)).

Extensions

More terms from Don Reble, May 16 2002

A090951 LCM of the first n numbers of the form p^q, where p and q are 1 or prime.

Original entry on oeis.org

1, 2, 6, 12, 60, 420, 840, 2520, 27720, 360360, 6126120, 116396280, 2677114440, 13385572200, 40156716600, 1164544781400, 36100888223400, 144403552893600, 5342931457063200, 219060189739591200, 9419588158802421600
Offset: 1

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Author

Russell Easterly, Feb 26 2004

Keywords

Comments

Is the sum of the series 1/a(n) transcendental?

Examples

			a(11) = 6126120 = 1*2*3*2*5*7*2*3*11*13*17.

Crossrefs

Cf. A051451.

Extensions

Edited and extended by David Wasserman, Mar 13 2006

A274461 Least common multiple of first n proper prime powers.

Original entry on oeis.org

1, 4, 8, 72, 144, 3600, 10800, 21600, 1058400, 2116800, 6350400, 768398400, 3841992000, 7683984000, 1298593296000, 3895779888000, 7791559776000, 2251760775264000, 15762325426848000, 5690199479092128000, 11380398958184256000, 6020231048879471424000, 30101155244397357120000, 90303465733192071360000
Offset: 0

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Author

Franklin T. Adams-Watters, Jun 23 2016

Keywords

Comments

Squares in this sequence include a(0)=1^2, a(1)=2^2, a(4)=12^2, a(5)=60^2, a(10)=2520^2, and a(11)=27720^2. Are there any more?
All terms in this sequence are powerful numbers (A001694).

Crossrefs

Cf. A051451, A246547, A001694.

Programs

  • Mathematica
    t = Join[{1}, Select[Range@ 1000, Min@ FactorInteger[#][[All, 2]] > 1 &]]; Union@ Table[LCM @@ t[[1 ;; n]], {n, 45}] (* Michael De Vlieger, Jun 24 2016, after Harvey P. Dale at A001694 *)
  • PARI
    alist(n)=my(pp=0,x=1);vector(n,k,while(isprimepower(pp++)<2&&pp!=1,0); x=lcm(x, pp))

A298410 Unique least common multiples for {1,2,...,n}.

Original entry on oeis.org

2, 6, 12, 420, 840, 720720, 72201776446800, 6676878045498705789701874602220118271269436344024536000, 16674490806895842671659008751776385350270324508909651849955453691538889375930032935391666564679008085339616000
Offset: 1

Views

Author

Adrian Pietkiewicz, Jan 18 2018

Keywords

Comments

This is a subset of A003418 such that lcm(1,2,...,n-1) <> lcm(1,2,...,n) <> lcm(1,2,...,n+1) for (n>=1).
lcm(1,2,...,n) will be unique if both n and n+1 can be expressed as different prime powers, i.e., n = p^a and n+1 = q^b where p,q are prime and a,b are integers.

Examples

			lcm(1,2,...,7) is 420 and lcm(1,2,...,7,2^3) is 840 so 420 and 840 are in the sequence.
But lcm(1,2,...,7,2^3,3^2) = lcm(1,2...,7,2^3,3^2,(2*5)) = 2520. If n=9, n+1 is not a prime power and 2520 is not unique. So 2520 is not in the sequence.

Crossrefs

Cf. A003418, A051451, A134459.

Formula

a(n) = A003418(A134459(n)). - Michel Marcus, Jan 23 2018
Previous Showing 61-64 of 64 results.

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