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A128465
Numbers k such that k divides the numerator of alternating Harmonic number H'((k+1)/2) = A058313((k+1)/2).
1
1, 5, 7, 71, 379, 2659
OFFSET
1,2
COMMENTS
For k > 1 all 5 listed terms are primes.
The only known numbers k such that k divides the numerator of alternating Harmonic number H'((k-1)/2) = A058313((k-1)/2) are the Wieferich primes (A001220): 1093 and 3511.
An odd prime p = prime(n) belongs to this sequence iff Fermat quotient A007663(n) == A130912(n) == 2*(-1)^((p+1)/2) (mod p). - Max Alekseyev, Nov 30 2022
LINKS
Eric Weisstein's World of Mathematics, Harmonic Number
MATHEMATICA
f=0; Do[ f = f + (-1)^(n+1)*1/n; g = Numerator[f]; If[ IntegerQ[ g/(2n-1) ], Print[2n-1]], {n, 1, 3000} ]
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Mar 10 2007
EXTENSIONS
Edited by Max Alekseyev, Nov 30 2022
STATUS
approved