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Numbers k such that gcd(A001008(k), A001008(floor(k/2))) > 1.
12

%I #36 Aug 24 2021 13:08:45

%S 7,546,1092,1755,3510,4896,52447,670668

%N Numbers k such that gcd(A001008(k), A001008(floor(k/2))) > 1.

%C Note a connection to the Wieferich primes A001220: a(2) = (A001220(1) - 1)/2, a(3) = A001220(1) - 1, a(4) = (A001220(2) - 1)/2, a(5) = A001220(2) - 1. [Comment regarding a(2) added by _Kevin J. Gomez_, Jul 11 2017]

%C a(9) > 840000. - _Giovanni Resta_, May 13 2016

%t Select[Range[5000], GCD @@ Numerator@ HarmonicNumber@{#, Floor[#/2]} > 1 &] (* _Giovanni Resta_, May 13 2016 *)

%o (PARI) a001008(n)=numerator(sum(i=1, n, 1/i))

%o for(n=1, 1e6, if(gcd(a001008(n), a001008(n/2)) > 1, print1(n, ", "))) \\ _Felix Fröhlich_, Aug 08 2014

%Y The corresponding GCDs are given by A126197.

%Y Cf. A001008, A001220, A002805, A058312, A058313, A074791, A121594, A125581.

%K nonn,more

%O 1,1

%A _Max Alekseyev_ and _Tanya Khovanova_, Mar 07 2007, corrected Mar 10 2007

%E a(8) from _Giovanni Resta_, May 13 2016