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Search: id:A055468
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| A055468 |
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Composite numbers for which Sum of EulerPhi and Divisor-Sum is an integer multiple of the 4th power of the number of divisors. |
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+0
1
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| 1, 121, 125, 511, 767, 895, 1535, 1919, 2047, 2559, 2815, 3071, 3199, 3327, 3455, 3711, 3839, 4223, 4351, 4479, 4607, 4735, 4863, 5262, 5631, 5726, 5759, 5902, 5966, 6014, 6527, 7167, 7295, 7423, 7679, 7807, 8063, 9599, 9727, 9819, 9983, 10239
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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 special cases k differs from n and Phi+Sigma is divisible with higher powers of the number of divisors
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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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Integer solutions of Phi[x]+Sigma[x] = kd[x]^4 or A000203(n)+A000010(n) = k*A000005(n)^4, where k is integer.
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EXAMPLE
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n = 511 with 4 divisors,Sigma(511) = 592, Phi(511) = 432, 592+432 = 1024 = k*4^4, where k = 4
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CROSSREFS
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A000005, A000010, A000203.
Sequence in context: A014735 A137850 A036231 this_sequence A134328 A113614 A134941
Adjacent sequences: A055465 A055466 A055467 this_sequence A055469 A055470 A055471
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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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