A126563 Numbers k such that the ratio of A117731(k) and A082687(k) is composite.

119, 735, 5145, 36015, 252105, 1764735, 12353145

Offset: 1

Author

Alexander Adamchuk, Mar 12 2007, Jun 09 2007

Keywords

• nonn
• hard
• more

Comments

a(1) = 7*17, a(2) = 3*5*7^2, a(3) = 3*5*7^3.

Corresponding composite terms in A125741 are {119, 49, 49, 49, 49, 49, 49, ...}.

A125741(n) is composite for n = {7, 16, 36, 91, 226, 510, 1131, ...}.

Links

• Eric Weisstein's World of Mathematics, Harmonic Number.
• Eric Weisstein's World of Mathematics, Hilbert Matrix.

Crossrefs

Cf. A082687, A117731, A125581, A125740, A125741, A126196, A126197.

Programs

Mathematica

h=0; Do[ h=h+1/(n+1)/(2n+1); f=Numerator[n*h]; g=Numerator[h]; If[ !Equal[f, g] && !PrimeQ[f/g], Print[ {n, f/g, FactorInteger[n], FactorInteger[f/g]} ] ], {n, 1, 10000} ]

PARI

f(n) = sum(k=1, n, 1/(n+k));
isok(k) = my(fk = f(k), q = numerator(k*fk)/numerator(fk)); (q!=1) && !isprime(q); \\ Michel Marcus, Mar 08 2023

Extensions

Edited by Max Alekseyev, Jul 12 2019

a(5)-a(7) from Jinyuan Wang, Jul 10 2025