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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.
10
60, 240, 960, 4092, 16368, 58254, 61440, 65472, 116508, 466032, 710400, 983040, 1864128, 3932160, 4190208, 67043328, 119304192, 268173312, 1908867072, 7635468288, 16106127360, 711488165526, 1098437885952, 1422976331052
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
a(25) > 4*10^12. - Giovanni Resta, Feb 26 2020
LINKS
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
KEYWORD
nonn,more
EXTENSIONS
a(19) from Jud McCranie, Nov 13 2001
a(20)-a(21) from Jud McCranie, Jan 29 2012
a(22)-a(24) from Giovanni Resta, Feb 26 2020
STATUS
approved