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.

A290728 Analog of A084848, replacing "quadratic residue" (X^2) with "value of X^2+X".

Original entry on oeis.org

1, 1, 2, 3, 4, 4, 6, 8, 12, 12, 12, 16, 24, 24, 36, 42, 44, 48, 72, 84, 96, 112, 144, 144, 168, 176, 264, 308, 288, 336, 432, 480, 504, 648, 672, 864, 960, 1008, 1008, 1056, 1232, 1584, 1760, 1848, 2376, 2016, 2592
Offset: 1

Views

Author

N. J. A. Sloane, Aug 10 2017

Keywords

Links

Crossrefs

Cf. A085635, A084848, A290727, A290731.

Programs

  • Mathematica
    a290731[n_] := Product[{p, e} = pe; If[p==2, 2^(e-1), 1 + Quotient[p^(e+1), (2p + 2)]], {pe, FactorInteger[n]}];
Reap[For[r = 2; k = 1, k <= 200000, k++, v = a290731[k]; t = v/k; If[t < r, r = t; Sow[v]]]][[2, 1]] (* Jean-François Alcover, Sep 13 2018, from PARI *)
  • PARI
    a290731(n)={my(f=factor(n));prod(i=1,#f~,my([p,e]=f[i,]);if(p==2,2^(e-1),1+p^(e+1)\(2*p+2)))} \\ from Andrew Howroyd
r=2;for(k=1,200000,v=a290731(k);t=v/k;if(tHugo Pfoertner, Aug 23 2018

Formula

a(n) = A290731(A290727(n)) - Hugo Pfoertner, Aug 23 2018

Extensions

More terms from Hugo Pfoertner, Aug 22 2018
Initial term added by Hugo Pfoertner, Aug 23 2018

A290729 Analog of A085635, replacing "quadratic residue" (X^2) with "value of X(3X-1)/2".

Original entry on oeis.org

1, 5, 7, 11, 13, 17, 19, 23, 25, 35, 55, 65, 77, 91, 119, 133, 143, 175, 275, 325, 385, 455, 595, 665, 715, 935, 1001, 1309, 1463, 1547, 1729, 1925, 2275, 2975, 3325, 3575, 4675, 5005, 6545, 7315, 7735, 8645
Offset: 1

Views

Author

N. J. A. Sloane, Aug 10 2017

Keywords

Comments

Positions k where R(k) = A290732(k)/k, achieves a new minimum.

Links

Crossrefs

Cf. A000326, A085635, A084848, A290727, A290728, A290730, A290732.

Programs

  • Mathematica
    a[n_] := Product[{p, e} = pe; If[p <= 3, p^e, (p^e - p^(e-1))/2 + (p^(e-1) - p^(Mod[e+1, 2]))/(2*(p+1)) + 1], {pe, FactorInteger[n]}];
r = 2; Reap[For[j=1, j <= 10^4, j = j+1, t = a[j]/j; If[tJean-François Alcover, Oct 02 2018, after Hugo Pfoertner *)
  • PARI
    a290732(n)={my(f=factor(n));prod(k=1,#f~,my([p,e]=f[k,]);if(p<=3,p^e,(p^e-p^(e-1))/2+(p^(e-1)-p^((e+1)%2))/(2*(p+1))+1))}
my(r=2);for(j=1,10001,my(t=a290732(j)/j);if(tHugo Pfoertner, Aug 26 2018

Extensions

a(1) corrected by Hugo Pfoertner, Aug 26 2018

A290730 Analog of A084848, replacing "quadratic residue" (X^2) with "value of X(3X-1)/2". a(n) = A290732(A290729(n)).

Original entry on oeis.org

1, 3, 4, 6, 7, 9, 10, 12, 11, 12, 18, 21, 24, 28, 36, 40, 42, 44, 66, 77, 72, 84, 108, 120, 126, 162, 168, 216, 240, 252, 280, 264, 308, 396, 440, 462, 594, 504, 648, 720, 756, 840, 1008, 1080, 1134, 1260, 1512, 1512, 1680, 2016
Offset: 1

Views

Author

N. J. A. Sloane, Aug 10 2017

Keywords

Links

Crossrefs

Cf. A000326, A085635, A084848, A290727, A290728, A290729, A290732.

Programs

  • Mathematica
    a290732[n_] := Product[{p, e} = pe; If[p <= 3, p^e, (p^e - p^(e-1))/2 + (p^(e-1) - p^(Mod[e+1, 2]))/(2*(p+1))+1], {pe, FactorInteger[n]}];
r = 2; Reap[For[j = 1, j <= 24001, j = j+1, w = a290732[j]; t = w/j; If[t < r, r = t; Sow[w]]]][[2, 1]] (* Jean-François Alcover, Oct 03 2018, after Hugo Pfoertner *)
  • PARI
    a290732(n)={my(f=factor(n));prod(k=1,#f~,my([p,e]=f[k, ]); if(p<=3,p^e,(p^e-p^(e-1))/2+(p^(e-1)-p^((e+1)%2))/(2*(p+1))+1))}
my(r=2);for(j=1,24001,my(w=a290732(j),t=w/j);if(tHugo Pfoertner, Aug 26 2018

Extensions

More terms from Hugo Pfoertner, Aug 23 2018
a(1), a(19) and a(38) corrected by Hugo Pfoertner, Aug 26 2018
Showing 1-3 of 3 results.

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

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