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Search: id:A130697
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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
1
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| 1, 3, 14, 32, 54, 1458, 3765, 5343, 10342, 57918, 72432, 134072
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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REFERENCES
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F. Luca and A. Sankaranarayanan, On numbers n such that phi(1)+...+phi(n) is a square, preprint, 2007.
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FORMULA
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Numbers n such that phi(1)+phi(2)+...+phi(n)=x^2 with some integer x.
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EXAMPLE
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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
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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
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Sequence in context: A014696 A071396 A032525 this_sequence A033991 A081269 A140064
Adjacent sequences: A130694 A130695 A130696 this_sequence A130698 A130699 A130700
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KEYWORD
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nonn
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AUTHOR
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Florian Luca (fluca(AT)matmor.unam.mx), Jul 11 2007
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