%I
%S 4680,60192,179424,1737000,2578968,3441888,5604192,6008184,6331104,
%T 302459850,320457888,477229032,589459104,731925000,766073448,928765600
%N ftriperfect numbers, where f(n) = sigma(n) and ftriperfect numbers are defined similarly to fperfect numbers in A066218.
%C n is ftriperfect iff sum_{k divides n} f(k) = 3*f(n). ftriperfect numbers appear to be rare for many f. For the usual f(n) = n, there are at least 6 ftriperfect numbers known < 3.2 x 10^10, the first being 120. However, there are no ftriperfect numbers < 10^6 for f(n) = n+1 and f(n) = n1 (if one ignores the trivial n = 1).
%C Also numbers n such that 2*sigma(n) is equal to the sum of the divisors of their aliquot parts.  _Paolo P. Lava_, Jul 13 2016
%D Wells, D. Curious and Interesting Numbers, Revised Edition. Penguin Books, 1997. (See the entry on "120".)
%e Divisors of 4680 = {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 18, 20, 24, 26, 30, 36, 39, 40, 45, 52, 60, 65, 72, 78, 90, 104, 117, 120, 130, 156, 180, 195, 234, 260, 312, 360, 390, 468, 520, 585, 780, 936, 1170, 1560, 2340, 4680}; f applied to these yield {1, 3, 4, 7, 6, 12, 15, 13, 18, 28, 14, 24, 39, 42, 60, 42, 72, 91, 56, 90, 78, 98, 168, 84, 195, 168, 234, 210, 182, 360, 252, 392, 546, 336, 546, 588, 840, 1170, 1008, 1274, 1260, 1092, 2352, 2730, 3276, 5040, 7644, 16380}, which sum to 49140 = 3 * 16380 = 3 * f(4680). Hence 4680 is a term of the sequence.
%t f[x_] := DivisorSigma[1, x]; Do[If[ Apply[ Plus, Map[ f, Divisors[ n ] ] ] == 3*f[n], Print[n]], {n, 1, 10^7}]
%Y Cf. A066218.
%K nonn
%O 1,1
%A _Joseph L. Pe_, Jan 15 2002
%E a(5)a(16) from _Giovanni Resta_, Jul 13 2016
