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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• more

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

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

Crossrefs

Cf. A019278, A019279.

Formula

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

Extensions

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