A068584 Numbers k such that the denominator of (Sum_{j=1..k} 1/j)^2 equals the denominator of Sum_{j=1..k} 1/j^2.

1, 2, 3, 4, 5, 9, 15, 16, 17, 28, 29, 30, 31, 32, 49, 91, 92, 93, 94, 95, 96, 97, 98, 99, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 243, 244, 245, 246, 247, 248, 249, 968, 969, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 980, 981, 982, 983, 984

Offset: 1

Author

Benoit Cloitre, Mar 27 2002

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002805, A007407.

Programs

Mathematica

s = {}; sum1 = sum2 = 0; Do[sum1 += 1/j; sum2 += 1/j^2; If[Denominator[sum1^2] == Denominator[sum2], AppendTo[s, j]], {j, 1, 1000}]; s (* Amiram Eldar, Feb 18 2021 *)

PARI

isok(k) = denominator(sum(j=1, k, 1/j)^2) == denominator(sum(j=1, k, 1/j^2)); \\ Michel Marcus, Feb 15 2021

Formula

Numbers k such that A002805(k)^2 = A007407(k).