A129076 -id:A129076 - cp's OEIS frontend

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

N. J. A. Sloane

nonn

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

			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.

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

Cf. A019276, A019278, A019292, A129076.

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

Corrected by Michel Marcus, Apr 29 2017

A162964 a(n) = sigma(sigma(sigma(sigma(sigma(n))))).

Original entry on oeis.org

1, 15, 24, 60, 120, 360, 168, 480, 168, 360, 360, 1170, 480, 1512, 1512, 210, 360, 1170, 728, 1680, 576, 480, 1512, 4800, 210, 1680, 1344, 3276, 992, 2016, 576, 1651, 1560, 3276, 1560, 1512, 1512, 4800, 3276, 4064, 1680, 5952, 1560, 5040, 4800, 2016, 1560, 5040

Offset: 1

Jaroslav Krizek, Jul 19 2009

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to sigma(n)

Cf. A000203, A129076, A066971, A051027.

Cf. also A049107.

with(numtheory); f:=n->sigma(sigma(sigma(sigma(sigma(n))))); [seq(f(n),n=1..100)];

Table[Nest[DivisorSigma[1,#]&,n,5],{n,50}] (* Harvey P. Dale, Apr 19 2013 *)

A162964(n) = sigma(sigma(sigma(sigma(sigma(n))))); \\ Antti Karttunen, Nov 18 2017

a(n) = A000203(A000203(A000203(A000203(A000203(n))))).

More terms from N. J. A. Sloane, Mar 20 2010

cp's OEIS Frontend

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.

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