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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A029972

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

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Last modified July 22 03:22 EDT 2017. Contains 289648 sequences.