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A126563
Numbers k such that the ratio of A117731(k) and A082687(k) is composite.
0
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
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
KEYWORD
bref,hard,more,nonn
AUTHOR
Alexander Adamchuk, Mar 12 2007, Jun 09 2007
EXTENSIONS
Edited by Max Alekseyev, Jul 12 2019
STATUS
approved