A179891 Composites h such that antiharmonic mean B(h) of the numbers k < h such that gcd(k, h) = 1 is not integer.

4, 6, 8, 9, 12, 14, 15, 16, 18, 20, 21, 24, 25, 26, 27, 28, 30, 32, 33, 35, 36, 38, 39, 40, 42, 44, 45, 48, 49, 50, 51, 52, 54, 56, 57, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 84, 86, 87, 88, 90, 92, 93, 95, 96, 98, 99, 100, 102, 104, 105, 108, 111

Offset: 1

Author

Jaroslav Krizek, Jul 30 2010

Keywords

• nonn

Comments

Composites h such that B(h) = A053818(h) / A023896(h) = A175505(h) / A175506(h) is not integer.

Composites h such that A175506(h) > 1.

Subsequence of A179872.

A179872 is the union of this sequence and A007645.

Examples

			a(6) = 14 because B(14) = A053818(14) / A023896(14) = 406/42 = 29/3 (not integer).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1749 from G. C. Greubel)

Crossrefs

Cf. A007645, A023896, A053818, A175505, A175506.

Cf. A179871, A179872, A179873, A179874, A179875, A179876, A179877, A179878, A179879, A179880, A179882, A179883, A179884, A179885, A179886, A179887, A179890.

Programs

Mathematica

f[n_] := 2 Plus @@ (Select[ Range@n, GCD[ #, n] == 1 &]^2)/(n*EulerPhi@n); Select[ Range@ 111, ! PrimeQ@# && ! IntegerQ@f@# &] (* Robert G. Wilson v, Aug 02 2010 *)

PARI

isok(k) = if(isprime(k), 0, my(f = factor(k)); if(k == 1, 0, denominator(2*k/3 + (1/3) * prod(i = 1, #f~, 1 - f[i, 1])/eulerphi(f)) > 1)); \\ Amiram Eldar, May 25 2025

Extensions

More terms from Robert G. Wilson v, Aug 02 2010