A125745 Numbers k such that the numerator of Sum_{j=1..k} k^2/(2*j*(j+k)) is prime.

2, 3, 4, 5, 6, 7, 12, 35, 43, 73, 77, 93, 98, 151, 166, 224, 255, 372, 596, 602, 813, 934, 1139, 1373, 1397, 1411, 1530, 1892, 1954, 2236, 2275, 2930, 3209, 3257, 3420, 4493, 5002, 5553, 6173, 6599, 7615, 8601, 8785, 10895, 10923, 11161, 12118, 14451, 15741

Offset

1,1

Comments

Posted in response to a question from Dirk Boland.

Links

Table of n, a(n) for n=1..49.

Example

a(7) = 12 is a term because Sum_{j=1..k} k^2/(2*j*(j+k)) = 13013256143/892371480, for k=12, 13013256143 is prime and this is the 7th such sum with a prime numerator.

Mathematica

q[n_] := PrimeQ[Numerator[Sum[n^2/(2*j*(j + n)), {j, 1, n}]]]; Select[Range[1000], q] (* Amiram Eldar, Feb 19 2022 *)

Prog

(PARI) {ls=[]; for(k=1, 250, if(ispseudoprime(numerator(sum(j=1, k, k^2/(2*j*(j+k))))), ls=concat(ls, k))); print(ls)}

Crossrefs

Sequence in context: A033079 A173819 A165305 * A265124 A032990 A060810

Adjacent sequences: A125742 A125743 A125744 * A125746 A125747 A125748

Keyword

nonn

Author

David Broadhurst, Dec 05 2006

Extensions

a(30)-a(49) from Amiram Eldar, Feb 19 2022

Status

approved