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

1,1

Comments

Subsequence of A127061. - Max Alekseyev, Feb 08 2007

Links

Table of n, a(n) for n=1..39.

Formula

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A215315 A065725 A057468 * A214735 A216061 A348062

Adjacent sequences: A127059 A127060 A127061 * A127063 A127064 A127065

Keyword

nonn

Author

Artur Jasinski, Jan 04 2007

Extensions

More terms from Max Alekseyev, Feb 08 2007

Status

approved