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

1,2

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.

Links

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

Example

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

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 *)

Prog

(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

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.

Sequence in context: A109958 A053361 A214153 * A339003 A017641 A232540

Adjacent sequences: A179884 A179885 A179886 * A179888 A179889 A179890

Keyword

nonn

Author

Jaroslav Krizek, Jul 30 2010, Jul 31 2010

Extensions

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

Status

approved