

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.


12




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(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 * 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

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.
Index entries for sequences where any odd perfect numbers must occur


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.
Cf. A000203, A000396, A005820, A051027, A326051, A326181.
Sequence in context: A172437 A160283 A325994 * A331365 A300603 A301328
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



