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URL: https://oeis.org/A064279

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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.
3
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, 193, 1476, 1, 1168, 537, 1444, 1, 1728, 1, 1372
OFFSET
1,4
COMMENTS
For a prime p: a(p) = 1.
LINKS
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
Sequence in context: A019304 A072869 A369905 * A369908 A078710 A175763
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
Terms a(65..74) from Antti Karttunen, Jan 22 2025
STATUS
approved