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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. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A255842 A229966 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

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Last modified July 22 07:23 EDT 2019. Contains 325216 sequences. (Running on oeis4.)