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.

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

Author

Artur Jasinski, Jan 04 2007

Keywords

• nonn

Links

• Artur Jasinski & Michel Marcus, Table of n, a(n) for n = 1..60

Crossrefs

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

Programs

Mathematica

With[{nn=10000},Select[Flatten[Position[Denominator[Thread[{Accumulate[1/ Range[ nn]^2], Accumulate[ 1/Range[nn]^3]}]],?(IntegerQ[Sqrt[First[#]]] && IntegerQ[Surd[Last[#],3]]&),{1},Heads->False]],PrimeQ]] (* _Harvey P. Dale, Mar 05 2014 *)

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), print1(p, ", ")););} \\ Michel Marcus, Nov 05 2013

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