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A333170
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a(n) = Sum_{k=0..n} phi(k^2 + 1), where phi is the Euler totient function (A000010).
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2
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1, 2, 6, 10, 26, 38, 74, 94, 142, 182, 282, 342, 454, 518, 714, 826, 1082, 1194, 1434, 1614, 2014, 2206, 2590, 2798, 3374, 3686, 4362, 4650, 5274, 5694, 6526, 6958, 7758, 8190, 9246, 9858, 11154, 11698, 12786, 13546, 15146, 15958, 17366, 18086, 19862, 20874
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OFFSET
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0,2
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REFERENCES
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Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 166.
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LINKS
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FORMULA
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a(n) ~ (H/4) * n^3, where H = Product_{p prime, p == 1 (mod 4)} (1 - 2/p^2) = 0.8948412245... (A335963).
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EXAMPLE
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a(0) = phi(0^2 + 1) = phi(1) = 1.
a(1) = phi(0^2 + 1) + phi(1^2 + 1) = phi(1) + phi(2) = 1 + 1 = 2.
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MATHEMATICA
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Accumulate @ Table[EulerPhi[k^2 + 1], {k, 0, 100}]
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PROG
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(PARI) a(n) = sum(k=0, n, eulerphi(k^2+1)); \\ Michel Marcus, Mar 10 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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