A019292 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 (3,k)-perfect numbers.

1, 12, 14, 24, 52, 98, 156, 294, 684, 910, 1368, 1440, 4480, 4788, 5460, 5840, 6882, 7616, 9114, 14592, 18288, 22848, 32704, 40880, 52416, 53760, 54864, 56448, 60960, 65472, 94860, 120960, 122640, 169164, 185535, 186368, 194432, 196137, 201872, 208026, 286160

Offset

1,2

Comments

Currently, up to k=50, the least integers to be (3,k)-perfect numbers are: 1, ?, ?, ?, 52, 98, ?, ?, ?, 12, ?, 14, ?, 5840, 7616, 294, ?, 201872, 169164, 24, 684, ?, ?, 910, ?, 40880, 60960, 4480, ?, 4788, 316160, 185535, 3138192, 1440, 186368, 5460, ?, 208026, 194432, 1454544, 481057305600, 26873600, 13225790247247872, 1937376, 10905024, ?, ?, 94860, ?, 683956224. - Michel Marcus, Jun 04 2017

Links

Michel Marcus, Table of n, a(n) for n = 1..131

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

Michel Marcus, Unexhaustive list of terms

Example

14 is a term because applying sigma three times we see that 14 -> 24 -> 60 -> 168, and 168 = 12*14. So 14 is a (3,12)-perfect number. - N. J. A. Sloane, May 29 2017

Prog

(PARI) isok(n) = denominator(sigma(sigma(sigma(n)))/n) == 1; \\ Michel Marcus, Jan 02 2017

Crossrefs

Cf. A019278 ((2,k)-perfect numbers), A019293.

Sequence in context: A229966 A342491 A101557 * A175886 A181451 A022326

Adjacent sequences: A019289 A019290 A019291 * A019293 A019294 A019295

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Michel Marcus, Jan 02 2017

Status

approved