A179878 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 an integer (see A179882).

2, 11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 266, 347, 359, 383, 455, 467, 470, 479, 494, 503, 506, 518, 563, 587, 590, 719, 782, 839, 863, 887, 890, 902, 911, 935, 983, 986, 1019, 1166, 1178, 1187, 1235, 1283, 1295, 1307, 1319, 1334, 1358, 1367, 1394

Offset: 1

Author

Jaroslav Krizek, Jul 30 2010, Jul 31 2010

Keywords

• nonn

Comments

For corresponding values of numbers h-1 see A179877. Subsequence of A179876, A179871 and A179883.

Links

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

Crossrefs

Cf. A179871, A179872, A179873, A179874, A179875, A179876, A179877, A179879, A179880, A179882, A179883, A179884, A179885, A179886, A179887, A179890, A179891.

Programs

Mathematica

With[{s = Partition[Table[Mean[#^2]/Mean[#] &@ Select[Range[n - 1], GCD[#, n] == 1 &], {n, 1400}], 2, 1]}, 1 + Position[s, ?(And[IntegerQ@ First@ #, SameQ @@ #] &), 1, Heads -> False][[All, 1]]] (* _Michael De Vlieger, Jul 30 2018 *)

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) = {if(k == 1, 0, my(ah1 = ah(k), ah2 = ah(k-1)); ah1 == ah2 && denominator(ah1) == 1);} \\ Amiram Eldar, May 24 2025

Formula

a(n) = A179877(n) + 1. - Amiram Eldar, May 24 2025