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%I #36 Jun 04 2017 08:05:31
%S 1,12,14,24,52,98,156,294,684,910,1368,1440,4480,4788,5460,5840,6882,
%T 7616,9114,14592,18288,22848,32704,40880,52416,53760,54864,56448,
%U 60960,65472,94860,120960,122640,169164,185535,186368,194432,196137,201872,208026,286160
%N 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.
%C 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
%H Michel Marcus, <a href="/A019292/b019292.txt">Table of n, a(n) for n = 1..131</a>
%H Graeme L. Cohen and Herman J. J. te Riele, <a href="http://projecteuclid.org/euclid.em/1047565640">Iterating the sum-of-divisors function</a>, Experimental Mathematics, 5 (1996), pp. 93-100.
%H Michel Marcus, <a href="/A019292/a019292_1.log.txt">Unexhaustive list of terms</a>
%e 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
%o (PARI) isok(n) = denominator(sigma(sigma(sigma(n)))/n) == 1; \\ _Michel Marcus_, Jan 02 2017
%Y Cf. A019278 ((2,k)-perfect numbers), A019293.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Michel Marcus_, Jan 02 2017
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