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A206708
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Numbers k such that sigma(k) = sigma(sigma(k)-k).
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6
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6, 28, 220, 284, 496, 1184, 1210, 2620, 2924, 5020, 5564, 6232, 6368, 8128, 10744, 10856, 12285, 14595, 17296, 18416, 63020, 66928, 66992, 67095, 69615, 71145, 76084, 79750, 87633, 88730, 100485, 122265, 122368, 123152, 124155, 139815, 141664, 142310, 153176
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OFFSET
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1,1
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COMMENTS
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For all k, let s(k) = sigma(k) - k, the aliquot sum function A001065; then this sequence is the set of k such that s(s(k)) = k. - Jeppe Stig Nielsen, Jan 12 2020
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LINKS
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FORMULA
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Equals {A063990} union {A000396} = (amicable numbers) union (perfect numbers).
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EXAMPLE
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220 is in the sequence because sigma(220) = 504, sigma(504 - 220) = sigma(284) = 504.
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MAPLE
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q:= n-> (s-> s(n)=s(s(n)-n))(numtheory[sigma]):
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MATHEMATICA
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Select[Range[10^6], DivisorSigma[1, #]==DivisorSigma[1, DivisorSigma[1, #]-#]&]
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PROG
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(PARI) isok(k) = if (k != 1, my(sk=sigma(k)); sk == sigma(sk-k)); \\ Michel Marcus, Jun 24 2019
(Magma) [k:k in [2..154000]|s eq DivisorSigma(1, s-k) where s is DivisorSigma(1, k)]; // Marius A. Burtea, Jan 13 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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