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Search: id:A055465
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| A055465 |
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Composite numbers for which sum of EulerPhi and Divisor-Sum is an integer multiple of the number of divisors. |
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+0
1
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| 1, 4, 15, 21, 25, 30, 33, 35, 39, 45, 48, 49, 51, 55, 56, 57, 65, 69, 70, 77, 78, 81, 85, 87, 91, 93, 95, 99, 102, 105, 110, 111, 115, 119, 121, 123, 125, 126, 129, 133, 135, 140, 141, 143, 145, 147, 153, 155, 159, 161, 165, 168, 169, 174, 177, 180, 182, 183, 184
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OFFSET
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1,2
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COMMENT
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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) In more general case k differs from n.
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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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FORMULA
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Composite integer solutions of Phi[x]+Sigma[x] = kd[x] or A000203(n)+A000010(n) = k*A000005(n), where k is integer.
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EXAMPLE
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It is true for all primes and some composites. n = 78, 8 divisors, Sigma = 168, Phi = 24, 168+24 = 192 = 8*24
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CROSSREFS
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Sequence in context: A166732 A022133 A100783 this_sequence A167293 A054308 A051531
Adjacent sequences: A055462 A055463 A055464 this_sequence A055466 A055467 A055468
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jun 27 2000
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