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A019285 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 (2,8)-perfect numbers. 2
60, 240, 960, 4092, 16368, 58254, 61440, 65472, 116508, 466032, 710400, 983040, 1864128, 3932160, 4190208, 67043328, 119304192, 268173312, 1908867072, 7635468288, 16106127360 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If 2^p-1 is a Mersenne prime greater than 3 then m = 15*2^(p-1) is in the sequence. Because sigma(sigma(m)) = sigma(15*2^(p-1)) = sigma(24*(2^p-1)) = 60*2^p = 8*(15*2^(p-1)) = 8*m. So for n>1 15/2*(A000668(n)+1) is in the sequence. 60, 240, 960, 61440, 983040, 3932160, 16106127360 and 1729382256910270464042 are such terms. - 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

1422976331052 is also a term. See comment in A019278. - Michel Marcus, May 15 2016

LINKS

Table of n, a(n) for n=1..21.

G. L. Cohen and H. J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.

PROG

(PARI) isok(n) = sigma(sigma(n))/n == 8; \\ Michel Marcus, May 15 2016

CROSSREFS

Cf. A000668, A019276, A019278, A019279, A019282, A019283, A019284.

Sequence in context: A103741 A140873 A263225 * A261970 A206144 A008428

Adjacent sequences:  A019282 A019283 A019284 * A019286 A019287 A019288

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

a(19) from Jud McCranie, Nov 13 2001

a(20)-a(21) from Jud McCranie, Jan 29 2012

STATUS

approved

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Last modified July 21 21:14 EDT 2019. Contains 325199 sequences. (Running on oeis4.)