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A055464
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Numbers n such that sum of EulerPhi and DivisorSum is an integer multiple of the number of divisors.
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1
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1, 2, 3, 4, 5, 7, 11, 13, 15, 17, 19, 21, 23, 25, 29, 30, 31, 33, 35, 37, 39, 41, 43, 45, 47, 48, 49, 51, 53, 55, 56, 57, 59, 61, 65, 67, 69, 70, 71, 73, 77, 78, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 102, 103, 105, 107, 109, 110, 111, 113, 115, 119, 121, 123
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OFFSET
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1,2
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COMMENTS
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Makowski proved that phi(n)+Sigma[n] = nd[n] iff n is a prime (see in Sivaramakrishnan, Chapter I, page 8, Theorem 3).
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REFERENCES
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Sivaramakrishnan, R. (1989): Classical Theory of Arithmetical Functions Marcel Dekker, Inc., New York-Basel.
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LINKS
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FORMULA
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EXAMPLE
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It is true for all primes and some composites. n = 99, 6 divisors, Sigma = 156, Phi = 60, 156+60 = 216 = 6*36, k = 36.
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MATHEMATICA
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okQ[n_]:=Divisible[EulerPhi[n]+DivisorSigma[1, n], DivisorSigma[0, n]]
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PROG
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(PARI) isok(n) = !((eulerphi(n) + sigma(n)) % numdiv(n)); \\ Michel Marcus, Dec 01 2017
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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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