A179887 Nonprimes q such that antiharmonic mean B(q) of the numbers k < q such that gcd(k, q) = 1 is an integer, where B(q) = A053818(q) / A023896(q) = A175505(q) / A175506(q).

1, 10, 22, 34, 46, 55, 58, 82, 85, 91, 94, 106, 110, 115, 118, 133, 142, 145, 166, 170, 178, 182, 187, 202, 205, 214, 217, 226, 230, 235, 247, 253, 259, 262, 265, 266, 274, 290, 295, 298, 301, 319, 334, 346, 355, 358, 374, 382, 391, 394, 403, 410, 415, 427

Offset: 1

Author

Jaroslav Krizek, Jul 30 2010, Jul 31 2010

Keywords

• nonn

Comments

Nonprimes q such that A175506(q) = 1.

Subsequence of A179871.

A179871 is the union of this sequence and A003627.

Corresponding values of B(q) in A179890.

Examples

			a(6) = 55 because B(55) = A053818(55) / A023896(55) = 40700 / 1100 = 37 (integer).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1653 from G. C. Greubel)

Crossrefs

Cf. A003627, A023896, A053818, A175505, A175506.

Cf. A179871, A179872, A179873, A179874, A179875, A179876, A179877, A179878, A179879, A179880, A179882, A179883, A179884, A179885, A179887, A179890, A179891.

Programs

Mathematica

f[n_] := 2 Plus @@ (Select[ Range@n, GCD[ #, n] == 1 &]^2)/(n*EulerPhi@n); Select[ Range@ 433, ! PrimeQ@# && IntegerQ@ f@# &] (* Robert G. Wilson v, Aug 02 2010 *)

PARI

isok(k) = if(isprime(k), 0, my(f = factor(k)); if(k == 1, 1, denominator(2*k/3 + (1/3) * prod(i = 1, #f~, 1 - f[i, 1])/eulerphi(f)) == 1)); \\ Amiram Eldar, May 26 2025

Extensions

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