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Search: id:A091340
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| A091340 |
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Amicable numbers with property that each member n of the corresponding amicable pair is divisible by sopfr(n) (sopfr: sum of prime factors with repetition). |
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| 821921625, 988676775, 4024942087978, 4179223134422, 100733767393275, 110452715806725
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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a(2n),a(2n+1) is a pair of amicable numbers for n=0,1,... For each a(m), m=0,1,...: sopfr(a(m)) divides a(m).
Conjecture: sequence is finite, even though there are quite a lot of known amicable numbers (about 6.0E6 currently).
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LINKS
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J.M. Pedersen, List of known amicable pairs
J. O. M. Pedersen, Tables of Aliquot Cycles
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EXAMPLE
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a(0): 821921625=3^2*5^3*7*29*59*61, sopfr(n) = 177 = 3*59
a(1): 988676775=3^2*5^2*71*199*311, sopfr(n) = 597 = 3*199
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CROSSREFS
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Cf. A001414.
Sequence in context: A104829 A017540 A132216 this_sequence A114665 A051470 A076135
Adjacent sequences: A091337 A091338 A091339 this_sequence A091341 A091342 A091343
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KEYWORD
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nonn
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AUTHOR
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Sven Simon (sven-h.simon(AT)t-online.de), Dec 31 2003
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