A179879 Numbers h such that h and h+1 have same antiharmonic mean of the numbers k < h such that gcd(k, h) = 1 and simultaneously this mean is not integer.

6, 65, 69, 77, 129, 185, 194, 210, 221, 237, 254, 309, 321, 330, 365, 398, 417, 437, 462, 473, 482, 497, 533, 546, 554, 570, 573, 581, 597, 614, 626, 662, 669, 681, 690, 714, 753, 758, 785, 789, 794, 813, 858, 893, 905, 914, 966, 993, 1037, 1073, 1094, 1101, 1122

Offset: 1

Author

Jaroslav Krizek, Jul 30 2010

Keywords

• nonn

Comments

Subsequence of A179875 and A179883.

For corresponding values of numbers h+1 see A179880. - Jaroslav Krizek, Jul 31 2010

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A179871, A179872, A179873, A179874, A179875, A179876, A179877, A179878, A179880, A179882, A179883, A179884, A179885, A179886, A179887, A179890, A179891.

Programs

PARI

ah(n) = {my(f = factor(n)); if(n == 1, 1, 2*n/3 + (1/3) * prod(i = 1, #f~, 1 - f[i, 1])/eulerphi(f));}
isok(k) = {my(ah1 = ah(k), ah2 = ah(k+1)); ah1 == ah2 && denominator(ah1) > 1;} \\ Amiram Eldar, May 24 2025

Formula

a(n) = A179880(n) - 1. - Jaroslav Krizek, Jul 31 2010

Extensions

a(36) corrected and more terms added by Amiram Eldar, May 24 2025