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 1-6 of 6 results.

A127044 Squares of denominators of Sum_{k=1..p-1} 1/k^2 for p in A127042.

Original entry on oeis.org

1, 2, 12, 60, 720720, 12252240, 80313433200, 2329089562800, 144403552893600, 5342931457063200, 718766754945489455304472257065075294400, 52573842877942565273243107104095419458814459401768000
Offset: 1

Views

Author

Artur Jasinski, Jan 03 2007

Keywords

Links

Crossrefs

Cf. A061002, A034602, A127029, A127042, A127043.

Programs

  • Mathematica
    a = {}; Do[If[Sqrt[Denominator[Sum[1/x^2, {x, 1, Prime[x] - 1}]]] == Floor[Sqrt[Denominator[Sum[1/x^2, {x, 1, Prime[x] - 1}]]]], AppendTo[a, Sqrt[Denominator[Sum[1/x^2, {x, 1, Prime[x] - 1}]]]]], {x, 1, 50}]; a

A127049 Primes p such that denominator of Sum_{k=1..p-1} 1/k^6 is a sixth power.

Original entry on oeis.org

2, 3, 5, 7, 17, 19, 41, 43, 47, 97, 127, 191, 193, 197, 199, 211, 223, 227, 229, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 991, 997, 1009, 1013, 1187, 1193, 1201, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3613, 3617, 3623, 3631
Offset: 1

Views

Author

Artur Jasinski, Jan 03 2007, Jan 04 2007

Keywords

Links

Crossrefs

Cf. A061002, A034602, A127029, A127042, A127043, A127044, A127046, A127047, A127048, A127049, A127051.

Programs

  • Mathematica
    d[n_] := Module[{}, su = 0; a = {}; For[i = 1, i <= n, i++, su = su + 1/ i^6; If[PrimeQ[i + 1] && IntegerQ[(Denominator[su])^(1/6)], AppendTo[a, i + 1]]]; a]; d[2000]
Select[Prime[Range[600]],IntegerQ[Surd[Denominator[Sum[1/k^6,{k,#-1}]], 6]]&] (* Harvey P. Dale, Aug 04 2019 *)

Extensions

Edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar

A127061 Primes p such that denominator of Sum_{k=1..p-1} 1/k^2 is a square and denominator Sum_{k=1..p-1} 1/k^3 is a cube.

Original entry on oeis.org

2, 3, 5, 17, 29, 31, 37, 41, 97, 439, 443, 449, 457, 461, 463, 1009, 1013, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4283, 4289, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511
Offset: 1

Views

Author

Artur Jasinski, Jan 04 2007

Keywords

Links

Crossrefs

Cf. A061002, A034602, A127029, A127042, A127043, A127044, A127046, A127047, A127048, A127049, A127051.

Programs

Formula

Intersection of A127042 and A127046. - Michel Marcus, Nov 05 2013

Extensions

More terms from Max Alekseyev, Feb 08 2007
Missing terms in the [9461, 9587] range inserted by Michel Marcus, Nov 05 2013

A127045 Primes p such that denominator of Sum_{k=1..p-1} 1/k^9 is a 9th power.

Original entry on oeis.org

2, 3, 5, 11, 13, 17, 29, 31, 37, 97, 127, 131, 251, 257, 263, 293, 431, 433, 439, 443, 449, 457, 461, 463, 467, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3797, 3803, 3821, 3823, 3833, 3907, 3911, 3917
Offset: 1

Views

Author

Artur Jasinski, Jan 04 2007

Keywords

Links

Crossrefs

Cf. A061002, A034602, A127029, A127042, A127043, A127044, A127046, A127047, A127048, A127049, A127051.

Programs

  • Mathematica
    d[n_] := Module[{}, su = 0; a = {}; For[i = 1, i <= n, i++, su = su + 1/ i^9; If[PrimeQ[i + 1], If[IntegerQ[(Denominator[su])^(1/9)], AppendTo[a, i + 1]]]]; a] d[2000]
Select[Flatten[Position[Denominator[Accumulate[1/Range[4000]^9]],?(IntegerQ[ Surd[ #,9]]&)]]+1,PrimeQ] (* _Harvey P. Dale, Aug 06 2022 *)

A127062 Primes p such that denominator of Sum_{k=1..p-1} 1/k^2 is a square and denominator Sum_{k=1..p-1} 1/k^3 is a cube and denominator Sum_{k=1..p-1} 1/k^4 is a fourth power.

Original entry on oeis.org

2, 3, 5, 17, 29, 31, 97, 439, 443, 449, 457, 461, 463, 1009, 1013, 24391, 24407, 24413, 24419, 24421, 24439, 24443, 24469, 24473, 24481, 117659, 117671, 117673, 117679, 117701, 117703, 117709, 117721, 117727, 117731, 117751, 117757, 117763, 117773
Offset: 1

Views

Author

Artur Jasinski, Jan 04 2007

Keywords

Comments

Subsequence of A127061. - Max Alekseyev, Feb 08 2007

Crossrefs

Cf. A061002, A034602, A127029, A127042, A127043, A127044, A127046, A127047, A127048, A127049, A127051, A127061.

Programs

  • Mathematica
    pdenQ[n_]:=Module[{c=Denominator[Table[Sum[1/k^i,{k,n-1}],{i,2,4}]]}, AllTrue[{ Surd[c[[1]],2], Surd[c[[2]],3],Surd[c[[3]],4]},IntegerQ]]; Select[Prime[Range[12000]],pdenQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 06 2015 *)
  • PARI
    lista(nn) = {forprime(p = 2, nn, if (issquare(denominator(sum(k=1, p-1, 1/k^2))) && ispower(denominator(sum(k=1, p-1, 1/k^3)),3) && ispower(denominator(sum(k=1, p-1, 1/k^4)),4), print1(p, ", ")););} \\ Michel Marcus, Nov 05 2013

Formula

Intersection of A127042, A127046 and A127047. - Michel Marcus, Nov 05 2013

Extensions

More terms from Max Alekseyev, Feb 08 2007

A127063 Primes p such that denominator of Sum_{k=1..p-1} 1/k^2 is a square and denominator Sum_{k=1..p-1} 1/k^3 is a cube and denominator Sum_{k=1..p-1} 1/k^4 is a fourth power and denominator Sum_{k=1..p-1} 1/k^5 is a fifth power.

Original entry on oeis.org

2, 3, 5, 17, 439, 443, 16400183, 16400191, 16400201, 16400203, 16400221, 16400231, 16400233, 16400269, 16400273, 16400299, 16400309, 16400317, 16400347, 16400383, 16400387, 16400389, 16400411, 16400413, 16400429, 16400431
Offset: 1

Views

Author

Artur Jasinski, Jan 04 2007

Keywords

Comments

Subsequence of A127062 and of A127061. - Max Alekseyev, Feb 08 2007

Crossrefs

Cf. A061002, A034602, A127029, A127042, A127043, A127044, A127046, A127047, A127048, A127049, A127051, A127061, A127062.

Extensions

More terms from Max Alekseyev, Feb 08 2007
Showing 1-6 of 6 results.

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