

A019283


Let sigma_m (n) be result of applying sumofdivisors function m times to n; call n (m,k)perfect if sigma_m (n) = k*n; sequence gives the (2,6)perfect numbers.


5




OFFSET

1,1


COMMENTS

If 2^p1 is a Mersenne prime then m = 21*2^(p1) is in the sequence. Because sigma(sigma(m)) = sigma(21*2^(p1)) = sigma(32*(2^p1)) = 63*2^p = 6*(21*2^(p1)) = 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 Cohente Riele links under A019276.
No other terms < 5 x 10^11.  Jud McCranie, Feb 08 2012


LINKS

Table of n, a(n) for n=1..10.
Graeme L. Cohen and Herman J. J. te Riele, Iterating the sumofdivisors function, Experimental Mathematics, 5 (1996), pp. 93100.


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

Cf. A000668, A019278, A019279, A019282.
Sequence in context: A153644 A172437 A160283 * A300603 A301328 A067296
Adjacent sequences: A019280 A019281 A019282 * A019284 A019285 A019286


KEYWORD

nonn,more


AUTHOR

N. J. A. Sloane.


EXTENSIONS

a(10) by Jud McCranie, Feb 08 2012


STATUS

approved



