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

1,1

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.

Links

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

Example

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

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 *)

Prog

(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

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.

Sequence in context: A176539 A285256 A013920 * A064590 A259315 A211771

Adjacent sequences: A179888 A179889 A179890 * A179892 A179893 A179894

Keyword

nonn

Author

Jaroslav Krizek, Jul 30 2010

Extensions

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

Status

approved