A126196 Numbers k such that gcd(A001008(k), A001008(floor(k/2))) > 1.

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

Offset: 1

Author

Max Alekseyev and Tanya Khovanova, Mar 07 2007, corrected Mar 10 2007

Keywords

• nonn
• more

Comments

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]

a(9) > 840000. - Giovanni Resta, May 13 2016

Crossrefs

The corresponding GCDs are given by A126197.

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

Programs

Mathematica

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

PARI

a001008(n)=numerator(sum(i=1, n, 1/i))
for(n=1, 1e6, if(gcd(a001008(n), a001008(n/2)) > 1, print1(n, ", "))) \\ Felix Fröhlich, Aug 08 2014

Extensions

a(8) from Giovanni Resta, May 13 2016