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.

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

Author

Artur Jasinski, Jan 04 2007

Keywords

• nonn

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