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A059046
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Numbers n such that sigma(n)-n divides n-1.
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1
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2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 77, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Primes and prime powers (A00961) satisfy this equation, but other numbers do also (A059047). This sequence is the union of A000961 and A059047. These are related to hyperperfect numbers (A034897) in the cited paper by te Riele.
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REFERENCES
| H. J. J. te Riele, "Rules for constructing hyperperfect numbers", Fibonacci Quarterly, 22(1)1984, 50-60. See equation (3), the set M*.
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LINKS
| H. J. J. te Riele, Rules for constructing hyperperfect numbers
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EXAMPLE
| For x=77, sigma(77)=96, 96-77=19, which divides 77-1.
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MATHEMATICA
| Select[Range[2, 250], Divisible[#-1, DivisorSigma[1, #]-#]&] [From Harvey P. Dale, Jan. 18, 2011]
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PROG
| (MAGMA) [n : n in [2..1000] | (n-1) mod (SumOfDivisors(n)-n) eq 0 ]; (from N. J. A. Sloane (njas(AT)research.att.com), Dec 23 2006)
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CROSSREFS
| Cf. A059047, A000203, A000961, A034897.
Sequence in context: A046686 A137944 A087441 * A144711 A036116 A000961
Adjacent sequences: A059043 A059044 A059045 * A059047 A059048 A059049
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KEYWORD
| nonn
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AUTHOR
| Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu), Dec 18 2000
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