A064279 Number of ordered pairs a,b of elements in the cyclic group C_n such that the subgroup generated by the pair a,b is a proper subgroup of C_n.

0, 1, 1, 4, 1, 12, 1, 16, 9, 28, 1, 48, 1, 52, 33, 64, 1, 108, 1, 112, 57, 124, 1, 192, 25, 172, 81, 208, 1, 324, 1, 256, 129, 292, 73, 432, 1, 364, 177, 448, 1, 612, 1, 496, 297, 532, 1, 768, 49, 700, 297, 688, 1, 972, 145, 832, 369, 844, 1, 1296, 1, 964, 513, 1024

Offset

1,4

Comments

For a prime p: a(p) = 1.

Links

Table of n, a(n) for n=1..64.

Formula

a(n) = n^2 - A007434(n) = n^2 - J_2(n).

G.f.: -Sum_{k>=2} mu(k) * x^k * (1 + x^k) / (1 - x^k)^3. - Ilya Gutkovskiy, Sep 14 2021

Mathematica

Table[a=GroupElements[CyclicGroup[n]]; n^2-Count[Flatten[Table[Table[GroupOrder[PermutationGroup[{a[[i]], a[[j]]}]], {i, 1, n}], {j, 1, n}]], n], {n, 1, 30}]  (* Geoffrey Critzer, Apr 14 2013 *)

Prog

(PARI)
A007434(n) = if(n<1, 0, sumdiv(n, d, d^2*moebius(n/d)));
a(n) = n^2 - A007434(n);  /* Joerg Arndt, Apr 14 2013 */

Crossrefs

Cf. A007434, A051953.

Sequence in context: A019304 A072869 A369905 * A369908 A078710 A175763

Adjacent sequences: A064276 A064277 A064278 * A064280 A064281 A064282

Keyword

nonn

Author

Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Sep 24 2001

Extensions

More terms from Vladeta Jovovic, Sep 25 2001

Status

approved