

A019293


Let sigma_m (n) be result of applying sumofdivisors function m times to n; call n (m,k)perfect if sigma_m (n) = k*n; sequence gives the (4,k)perfect numbers.


6



1, 2, 3, 4, 6, 8, 10, 12, 15, 18, 21, 24, 26, 32, 39, 42, 60, 65, 72, 84, 96, 160, 182, 336, 455, 512, 672, 896, 960, 992, 1023, 1280, 1536, 1848, 2040, 2688, 4092, 5472, 5920, 7808, 7936, 10416, 11934, 16352, 16380, 18720, 20384, 21824, 23424, 24564, 29127, 30240, 33792, 36720, 41440
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OFFSET

1,2


COMMENTS

Similarly to A019278, 2 and sigma(2) are both terms, and this can happen also for further iterations of sigma on known terms, thus providing new terms outside the current known range.  Michel Marcus, May 01 2017
Also it occurs that many divisors of A019278 are terms of this sequence.  Michel Marcus, May 28 2017


LINKS

Michel Marcus, Table of n, a(n) for n = 1..320
Graeme L. Cohen and Herman J. J. te Riele, Iterating the sumofdivisors function, Experimental Mathematics, 5 (1996), pp. 93100.
Michel Marcus, Unexhaustive list of terms


EXAMPLE

10 is a term because applying sigma four times we see that 10 > 18 > 39 > 168 > 120, and 120 = 12*10. So 10 is a (4,12)perfect number.


PROG

(PARI) isok(n) = denominator(sigma(sigma(sigma(sigma(n))))/n) == 1; \\ Michel Marcus, Apr 29 2017


CROSSREFS

Cf. A019276, A019278, A019292, A129076.
Sequence in context: A062418 A056168 A054041 * A130519 A001972 A005705
Adjacent sequences: A019290 A019291 A019292 * A019294 A019295 A019296


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

Corrected by Michel Marcus, Apr 29 2017


STATUS

approved



