A179873 Corresponding values of antiharmonic means B(h) to numbers h from A179871 (numbers h such that antiharmonic mean of the numbers k < h such that gcd(k, h) = 1 is an integer).

1, 1, 3, 7, 7, 11, 15, 15, 19, 23, 27, 31, 31, 35, 37, 39, 39, 47, 55, 55, 57, 59, 61, 63, 67, 71, 71, 73, 75, 77, 79, 87, 89, 91, 95, 97, 99, 111, 111, 113, 115, 119, 119, 121, 125, 127, 131, 135, 137, 143, 145, 151, 151, 153, 155, 157, 159, 165, 167, 169, 171

Offset: 1

Author

Jaroslav Krizek, Jul 30 2010, Jul 31 2010

Keywords

• nonn

Comments

Conjecture: nondecreasing sequence of odd numbers.

Examples

			a(6) = A175505(A179871(6)) = A175505(17) = 11 = B(17).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2500 from Ivan Neretin)

Crossrefs

Cf. A179871, A179872, A179874, A179875, A179876, A179877, A179878, A179879, A179880, A179882, A179883, A179884, A179885, A179886, A179887, A179890, A179891.

Programs

Mathematica

B[n_] := Plus @@ ((ks = Select[Range[n], GCD[n, #] == 1 &])^2)/Plus @@ ks; Select[B /@ Range[215], IntegerQ] (* Ivan Neretin, May 22 2015 *)

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));}
list(lim) = {my(m); for(k = 1, lim, m = ah(k); if(denominator(m) == 1, print1(m, ", ")));} \\ Amiram Eldar, May 25 2025

Formula

a(n) = A053818(A179871(n)) / A023896(A179871(n)) = A175505(A179871(n)).