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Search: id:A055467
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| A055467 |
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Composite numbers for which Sum of EulerPhi and Divisor-Sum is an integer multiple of the cube of the number of divisors. |
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+0
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| 1, 95, 99, 121, 125, 159, 287, 319, 415, 447, 511, 543, 654, 671, 703, 767, 799, 831, 895, 959, 1055, 1119, 1247, 1343, 1390, 1495, 1535, 1631, 1727, 1849, 1919, 1983, 2043, 2047, 2060, 2261, 2271, 2335, 2463, 2495, 2559, 2623, 2815, 2828, 2883, 2911
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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]^3 or A000203(n)+A000010(n) = k*A000005(n)^3, where k is integer.
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EXAMPLE
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n = 95 with 4 divisors,Sigma(95) = 120, Phi(95) = 72 72+120 = 192 = 3*4*4*4, k = 3
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CROSSREFS
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A000005, A000010, A000203.
Sequence in context: A093007 A033415 A067266 this_sequence A057654 A046005 A045121
Adjacent sequences: A055464 A055465 A055466 this_sequence A055468 A055469 A055470
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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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