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A060791
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a(n) = n / gcd(n,5).
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23
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1, 2, 3, 4, 1, 6, 7, 8, 9, 2, 11, 12, 13, 14, 3, 16, 17, 18, 19, 4, 21, 22, 23, 24, 5, 26, 27, 28, 29, 6, 31, 32, 33, 34, 7, 36, 37, 38, 39, 8, 41, 42, 43, 44, 9, 46, 47, 48, 49, 10, 51, 52, 53, 54, 11, 56, 57, 58, 59, 12, 61, 62, 63, 64, 13, 66, 67, 68, 69
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OFFSET
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1,2
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COMMENTS
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As well as being a multiplicative sequence, a(n) is also strong divisibility sequence, that is, gcd(a(n),a(m)) = a(gcd(n,m)) for n, m >= 1. In particular, a(n) is a divisibility sequence: if n divides m then a(n) divides a(m). Peter Bala, Feb 20 2019
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,2,0,0,0,0,-1).
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FORMULA
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G.f.: x*(1 + 2*x + 3*x^2 + 4*x^3 + x^4 + 4*x^5 + 3*x^6 + 2*x^7 + x^8)/(1 - x^5)^2.
a(n) = n/5 if 5|n, otherwise a(n) = n.
Dirichlet g.f.: zeta(s-1)*(1-4/5^s). (End)
G.f.: x*(x^4 + x^3 - x^2 + x + 1)*(x^4 + x^3 + 3*x^2 + x + 1)/((x - 1)^2*(x^4 + x^3 + x^2 + x + 1)^2). - R. J. Mathar, Oct 31 2015
a(n) = numerator(n/(n + 5)).
If gcd(n, m) = 1 then a(a(n)*a(m)) = a(a(n)) * a(a(m)), a(a(a(n))*a(a(m))) = a(a(a(n))) * a(a(a(m))) and so on.
G.f.: x/(1 - x)^2 - 4*x^5/(1 - x^5)^2. (End)
Sum_{k=1..n} a(k) ~ (21/50) * n^2. - Amiram Eldar, Nov 25 2022
Sum_{n>=1} (-1)^(n+1)/a(n) = 9*log(2)/5. - Amiram Eldar, Sep 08 2023
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MAPLE
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MATHEMATICA
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PROG
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(PARI) { for (n=1, 1000, write("b060791.txt", n, " ", n / gcd(n, 5)); ) } \\ Harry J. Smith, Jul 12 2009
(PARI) for (n=1, 1000, print1(n/(5-4*(n%5>0))", ")) \\ Zak Seidov, Feb 17 2011
(Magma) [n/GCD(n, 5): n in [1..100]]; // G. C. Greubel, Feb 20 2019
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CROSSREFS
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KEYWORD
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nonn,mult,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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