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A130697
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Numbers n such that the sum of the Euler functions of integers up to n is a square.
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0
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1, 3, 14, 32, 54, 1458, 3765, 5343, 10342, 57918, 72432, 134072, 1103584, 4984175, 9191040, 18399460, 49034273, 176485286, 423360893, 1432766906, 62342171276
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| In the preprint listed below it is shown that the sequence (a(n))_n is of asymptotic density zero as a subset of the positive integers. It is not known if the sequence is infinite.
a(22) > 10^11. - Donovan Johnson, Mar 15 2011
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REFERENCES
| F. Luca and A. Sankaranarayanan, On numbers n such that phi(1)+...+phi(n) is a square, preprint, 2007.
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FORMULA
| Numbers n such that phi(1)+phi(2)+...+phi(n)=x^2 with some integer x.
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EXAMPLE
| a(3)=14 since phi(1)+phi(2)+phi(3)+phi(4)+phi(5)+phi(6)+phi(7)+phi(8)+phi(9)+phi(10)+phi(11)+phi(12)+phi(14)=64=8^2
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MATHEMATICA
| T=0; For[l = 1, l < 1000000, l++, T = T + EulerPhi[l]; If[T == Floor[Sqrt[T]]^2, Print[l, " ", Floor[Sqrt[T]]]]]
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CROSSREFS
| Sequence in context: A071396 A032525 A197946 * A033991 A155154 A081269
Adjacent sequences: A130694 A130695 A130696 * A130698 A130699 A130700
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KEYWORD
| nonn
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AUTHOR
| Florian Luca (fluca(AT)matmor.unam.mx), Jul 11 2007
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EXTENSIONS
| a(13)-a(19) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Dec 02 2009
a(20)-a(21) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Mar 15 2011
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