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A062011
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Number of cyclic subgroups of the group C_n X C_2 (where C_n is the cyclic group with n elements).
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6
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2, 4, 4, 6, 4, 8, 4, 8, 6, 8, 4, 12, 4, 8, 8, 10, 4, 12, 4, 12, 8, 8, 4, 16, 6, 8, 8, 12, 4, 16, 4, 12, 8, 8, 8, 18, 4, 8, 8, 16, 4, 16, 4, 12, 12, 8, 4, 20, 6, 12, 8, 12, 4, 16, 8, 16, 8, 8, 4, 24, 4, 8, 12, 14, 8, 16, 4, 12, 8, 16, 4, 24, 4, 8, 12, 12, 8, 16, 4, 20, 10, 8, 4, 24, 8, 8, 8, 16
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Also number of divisors of p*n, where p is any prime not dividing n, e.g.: a(n) = A000005(A087560(n)) = A000005(A119416(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 17 2006
If p(x) is a polynomial with integer coefficients, and if r is an integer zero of p(x), then r is a divisor of the constant term c_0 of p(x). Under this theorem, p(x) can have a(c_0) possible integer roots. a(n) is also the number of integer divisor of n, while A000005(n) is the number of positive divisors. - Enrique Pérez Herrero, Jul 21 2011
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
| a(n) = 2*tau(n).
More generally, the number of cyclic subgroups of the group C_n X C_m is Sum_{i|n, j|m} phi(i)*phi(j)/phi(lcm(i, j)), where phi=Euler totient function, cf. A000010. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 15 2001
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MATHEMATICA
| A062011[n_] := 2*DivisorSigma[0, n]; Array[A062011, 50] (* Enrique Pérez Herrero - Jul 15 2011 *)
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PROG
| (PARI) { for (n=1, 1000, write("b062011.txt", n, " ", 2*numdiv(n)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 29 2009]
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CROSSREFS
| Cf. A060710, A000005, A060648.
Sequence in context: A049782 A091666 A084290 * A132857 A152782 A057696
Adjacent sequences: A062008 A062009 A062010 * A062012 A062013 A062014
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KEYWORD
| nonn,easy
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AUTHOR
| Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 12 2001
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 14 2001
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