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A019283 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. 14
42, 84, 160, 336, 1344, 86016, 550095, 1376256, 5505024, 22548578304 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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.
No other terms < 5 * 10^11. - Jud McCranie, Feb 08 2012
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
a(11) > 4*10^12. - Giovanni Resta, Feb 26 2020
LINKS
Graeme L. Cohen and Herman J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.
MATHEMATICA
Do[If[DivisorSigma[1, DivisorSigma[1, n]]==6n, Print[n]], {n, 6000000}] (* Farideh Firoozbakht, Dec 05 2005 *)
PROG
(PARI) isok(n) = sigma(sigma(n))/n == 6; \\ Michel Marcus, May 12 2016
CROSSREFS
Sequence in context: A160283 A325994 A352481 * A331365 A369275 A300603
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
a(10) by Jud McCranie, Feb 08 2012
STATUS
approved

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Last modified March 19 02:51 EDT 2024. Contains 370952 sequences. (Running on oeis4.)