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A058026
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Number of positive integers, k, where k <= n and GCD(k,n) = GCD(k+1,n) = 1.
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4
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1, 0, 1, 0, 3, 0, 5, 0, 3, 0, 9, 0, 11, 0, 3, 0, 15, 0, 17, 0, 5, 0, 21, 0, 15, 0, 9, 0, 27, 0, 29, 0, 9, 0, 15, 0, 35, 0, 11, 0, 39, 0, 41, 0, 9, 0, 45, 0, 35, 0, 15, 0, 51, 0, 27, 0, 17, 0, 57, 0, 59, 0, 15, 0, 33, 0, 65, 0, 21, 0, 69, 0, 71, 0, 15, 0, 45, 0, 77, 0, 27, 0, 81, 0, 45, 0, 27, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Called the Schemmel totient function in the Handbook of Number Theory II. - R. J. Mathar, Apr 15 2011
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FORMULA
| Multiplicative with a(p^e) = p^(e-1)*(p-2). - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 01 2001
Sum_{d|n} n/d*mu(d)*tau(d). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 29 2002
a(n) = Sum_{d divides n} phi(n/d)*(-1)^omega(d). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 26 2002
A003557(n) | a(n). - R. J. Mathar, Mar 30 2011
a(n) = n*product_{primes p|n} (1-2/p). Dirichlet g.f. zeta(s-1)*product_p (1-2*p^(-s)). - R. J. Mathar, Apr 15 2011
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EXAMPLE
| a(15) = 3 because 1 and 2, 7 and 8 and 13 and 14 are all relatively prime to 15.
a(15) = a(3*5) = a(3)*a(5) = 3^0*(3-2)*5^0*(5-2) = 3.
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MAPLE
| A058026 := proc(n) local a; a := n ; for p in numtheory[factorset](n) do a := a*(1-2/p) ; end do: a ; end proc: # R. J. Mathar, Apr 15 2011
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CROSSREFS
| Cf. A070554, A069828.
Sequence in context: A122274 A003966 A123931 * A004605 A175919 A086664
Adjacent sequences: A058023 A058024 A058025 * A058027 A058028 A058029
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KEYWORD
| nonn,mult
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AUTHOR
| Leroy Quet Nov 15 2000
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