A019284 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 (2,7)-perfect numbers.

24, 1536, 47360, 343976, 572941926400

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• more

Comments

See also the Cohen-te Riele links under A019276.

No other terms < 5*10^11. - Jud McCranie, Feb 08 2012

572941926400 is also a term. See comment in A019278. - Michel Marcus, May 15 2016

a(6) > 4*10^12, if it exists. - Giovanni Resta, Feb 26 2020

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. A000668, A019278, A019279, A019281, A019282, A019283, A019285, A019286, A019287, A019288, A019289, A019290, A019291.

Programs

Mathematica

Select[Range[50000], DivisorSigma[1, DivisorSigma[1, #]]/# == 7 &] (* Robert Price, Apr 07 2019 *)

PARI

isok(n) = sigma(sigma(n))/n  == 7; \\ Michel Marcus, May 12 2016

Extensions

a(5) from Giovanni Resta, Feb 26 2020