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

119, 735, 5145, 36015

Offset

1,1

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, ...}.

A125741(n) is composite for n = {7, 16, 36, ...}.

Links

Table of n, a(n) for n=1..4.

Eric Weisstein's World of Mathematics, Harmonic Number.

Eric Weisstein's World of Mathematics, Hilbert Matrix.

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} ]

Prog

(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

Crossrefs

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

Sequence in context: A351906 A367723 A373541 * A362320 A355377 A067134

Adjacent sequences: A126560 A126561 A126562 * A126564 A126565 A126566

Keyword

bref,hard,more,nonn

Author

Alexander Adamchuk, Mar 12 2007, Jun 09 2007

Extensions

Edited by Max Alekseyev, Jul 12 2019

Status

approved