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.

A080744 Smallest element of n-th row of A080743.

Original entry on oeis.org

1, 2, 3, 4, 5, 0, 7, 8, 9, 21, 11, 35, 13, 33, 26, 16, 17, 65, 19, 51, 38, 57, 23, 95, 25, 69, 27, 75, 29, 150, 31, 32, 62, 93, 96, 155, 37, 217, 74, 111, 41, 185, 43, 123, 86, 129, 47, 215, 49, 141, 98, 147, 53, 245, 106, 159, 212, 265, 59, 371, 61, 177, 122, 64, 244, 305
Offset: 1

Views

Author

N. J. A. Sloane, Mar 08 2003

Keywords

Links

Crossrefs

Cf. A008475, A051613, A080743, A051703.

Extensions

More terms from Vladeta Jovovic, Mar 09 2003

A051703 Maximal value of products of partitions of n into powers of distinct primes (1 not considered a power).

Original entry on oeis.org

1, 0, 2, 3, 4, 6, 0, 12, 15, 20, 30, 28, 60, 40, 84, 105, 140, 210, 180, 420, 280, 330, 360, 840, 504, 1260, 1155, 1540, 2310, 2520, 4620, 3080, 5460, 3960, 9240, 5544, 13860, 6552, 16380, 15015, 27720, 30030, 32760, 60060, 40040, 45045, 51480, 120120
Offset: 0

Views

Author

Vladeta Jovovic

Keywords

Examples

			a(11) = 28 because max{11, 2*3^2, 2^3*3, 2^2*7} = 28.

Links

Crossrefs

Largest element of n-th row of A080743.
A000793(n)=max{A000793(n-1), a(n)}, A000793(0)=1.
Cf. A008475, A051613, A080743, A080744, A051704.

Programs

  • Maple
    b:= proc(n, i) option remember; local p;
      p:= `if`(i<1, 1, ithprime(i));
      `if`(n=0, 1, `if`(i<1 or n<0, 0, max(b(n, i-1),
      seq(p^j*b(n-p^j, i-1), j=1..ilog[p](n))) ))
    end:
a:= n-> b(n, numtheory[pi](n)):
seq(a(n), n=0..60);  # Alois P. Heinz, Feb 16 2013
  • Mathematica
    nmax = 48; Do[a[n]=0, {n, 1, nmax}]; km = PrimePi[nmax]; For[k=1, k <= km, k++, q = 1; p = Prime[k]; For[i=nmax, i >= 1, i--, q=1; While[q*p <= i, q *= p; If[i == q, m = q, If[a[i - q] != 0, m = q*a[i - q], m = 0]]; a[i] = Max[a[i], m]]]]; a[0] = 1; Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Aug 02 2012, translated from Robert Gerbicz's Pari program *)
  • PARI
    {N=1000;v=vector(N,i,0);forprime(p=2,N,q=1;forstep(i=N,1,-1,
q=1;while(q*p<=i,q*=p;if(i==q,M=q,if(v[i-q],M=q*v[i-q],M=0));
v[i]=max(v[i],M))));print(0" "1);for(i=1,N,print(i" "v[i]))} \\ Robert Gerbicz, Jul 31 2012

Extensions

Corrected and extended by Robert Gerbicz, Jul 31 2012

A005417 Maximal period of an n-stage shift register.

Original entry on oeis.org

2, 6, 12, 30, 60, 120, 210, 420, 840, 1260, 2520, 2520, 5040, 9240, 13860, 27720, 32760, 55440, 65520, 120120, 180180, 360360, 360360, 720720, 720720, 942480, 1113840
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Maximal order of an element of finite order in GL(2n, Z) or GL(2n+1, Z).
a(n) is the max of the first n numbers in A080742.

References

  • H. Lüneburg, Galoisfelder, Kreisteilungskörper und Schieberegisterfolgen. B. I. Wissenschaftsverlag, Mannheim, 1979.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A000793, A080742, A080743.

Programs

  • Mathematica
    (* b,c = a080737 *)
nmax = 26;
kmax = 1200000; (* kmax increased by 100000 until results do not change *)
b[1] = b[2] = 0; b[p_?PrimeQ] := b[p] = p-1; b[k_] := b[k] = If[Length[f = FactorInteger[k]]==1, EulerPhi[k], Total[b /@ (f[[All, 1]]^f[[All, 2]])] ];
orders = Table[{k, b[k]}, {k, 1, kmax}];
c[0] = 2; c[n_] := c[n] = Select[orders, 2n-1 <= #[[2]] <= 2n&][[-1, 1]];
a[n_] := Table[c[m], {m, 0, n}] // Max;
Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Dec 17 2017 *)

Formula

a(n) = max m such that A067240(m) <= 2n + 1. E.g., a(2) = 12 since 12 is largest m such that A067240(m) <= 5.

Extensions

Entry revised by N. J. A. Sloane, Mar 10 2002
Showing 1-3 of 3 results.

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

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