A019280 - OEIS

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A019280

Let sigma_m(n) be result of applying the sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m(n) = k*n; sequence gives log_2 of the (2,2)-perfect numbers.

1, 2, 4, 6, 12, 16, 18, 30, 60

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OFFSET

1,2

COMMENTS

Cohen and te Riele prove that any even (2,2)-perfect number (a "superperfect" number) must be of the form 2^(p-1) with 2^p-1 prime (Suryanarayana) and the converse also holds. Any odd superperfect number must be a perfect square (Kanold). Searches up to > 10^20 did not find any odd examples. - Ralf Stephan, Jan 16 2003

See also the Cohen-te Riele links under A019276.

LINKS

Table of n, a(n) for n=1..9.

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

FORMULA

Coincides with A000043(n) - 1 unless odd superperfect numbers exist.

CROSSREFS

Cf. A019278, A019279.

Sequence in context: A050584 A260698 A309096 * A090748 A188047 A032465

Adjacent sequences: A019277 A019278 A019279 * A019281 A019282 A019283

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane

EXTENSIONS

a(8)-a(9) from Jud McCranie, Jun 01 2000

STATUS

approved