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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. 5
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(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 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 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

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

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Last modified November 16 17:06 EST 2018. Contains 317274 sequences. (Running on oeis4.)