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A019283
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Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,6)-perfect numbers.
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14
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OFFSET
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1,1
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COMMENTS
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If 2^p-1 is a Mersenne prime then m = 21*2^(p-1) is in the sequence. Because sigma(sigma(m)) = sigma(sigma(21*2^(p-1))) = sigma(32*(2^p-1)) = 63*2^p = 6*(21*2^(p-1)) = 6*m. So 21*(A000668+1)/2 is a subsequence of this sequence. This is the subsequence 42, 84, 336, 1344, 86016, 1376256, 5505024, 22548578304, 24211351596743786496, ... - Farideh Firoozbakht, Dec 05 2005
See also the Cohen-te Riele links under A019276.
Any odd perfect numbers must occur in this sequence, as such numbers must be in the intersection of A000396 and A326051, that is, satisfy both sigma(n) = 2n and sigma(2n) = 6n, thus in combination they must satisfy sigma(sigma(n)) = 6n. Note that any odd perfect number should occur also in A326181. - Antti Karttunen, Jun 16 2019
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LINKS
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MATHEMATICA
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Do[If[DivisorSigma[1, DivisorSigma[1, n]]==6n, Print[n]], {n, 6000000}] (* Farideh Firoozbakht, Dec 05 2005 *)
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PROG
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(PARI) isok(n) = sigma(sigma(n))/n == 6; \\ Michel Marcus, May 12 2016
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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