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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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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
| Sivaramakrishnan,R.(1989):Classical Theory of Arithmetical Functions Marcel Dekker,Inc., New York-Basel.
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FORMULA
| Solutions to Phi[x]+Sigma[x] = kd[x] or A000203(n)+A000010(n) = k*A000005(n), where k is integer.
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EXAMPLE
| 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
| okQ[n_]:=Divisible[EulerPhi[n]+DivisorSigma[1, n], DivisorSigma[0, n]]
Select[Range[125], okQ] (* From Harvey P. Dale, Mar 6 2011 *)
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CROSSREFS
| Sequence in context: A001729 A001087 A191876 * A139316 A062972 A036844
Adjacent sequences: A055461 A055462 A055463 * A055465 A055466 A055467
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jun 27 2000
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