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.

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

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 A328325

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