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

1,1

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

Formula

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

Prog

(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

Crossrefs

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

Sequence in context: A393765 A249896 A249828 * A350946 A297516 A389002

Adjacent sequences: A179876 A179877 A179878 * A179880 A179881 A179882

Keyword

nonn

Author

Jaroslav Krizek, Jul 30 2010

Extensions

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

Status

approved