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A019293 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 (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 (list; graph; refs; listen; history; text; internal format)
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 sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.

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

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Last modified July 21 17:20 EDT 2019. Contains 325198 sequences. (Running on oeis4.)