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

Author

N. J. A. Sloane

Keywords

• nonn

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

Examples

			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
		

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

Crossrefs

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

Programs

PARI

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

Extensions

More terms from Michel Marcus, Jan 02 2017