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A238533
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Number of solutions to gcd(x^2 + y^2 + z^2 + t^2 + h^2, n) = 1 with x,y,z,t,h in [0,n-1].
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10
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1, 16, 162, 512, 2500, 2592, 14406, 16384, 39366, 40000, 146410, 82944, 342732, 230496, 405000, 524288, 1336336, 629856, 2345778, 1280000, 2333772, 2342560, 6156502, 2654208, 7812500, 5483712, 9565938, 7375872, 19803868, 6480000, 27705630, 16777216, 23718420
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = phi(n^5) = n^4 * phi(n), where phi=A000010.
Dirichlet g.f.: zeta(s - 5) / zeta(s - 4). The n-th term of the Dirichlet inverse is n^4 * A023900(n) = (-1)^omega(n) * a(n) / A003557(n), where omega = A001221.
(End)
Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + p/(p^6 - p^5 - p + 1)) = 1.07162935672651489627... - Amiram Eldar, Dec 06 2020
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MATHEMATICA
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g[n_, 5] := g[n, 5] = Sum[If[GCD[x^2 + y^2 + z^2 + t^2 + h^2, n] == 1, 1, 0], {x, n}, {y, n}, {z, n}, {t, n}, {h, n}]; Table[g[n, 5] , {n, 1, 15}]
Table[n^4 * EulerPhi[n], {n, 1, 33}] (* Amiram Eldar, Dec 06 2020 *)
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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