cp's OEIS Frontend

A274339 The period 3 sequence of the iterated sum of deficient divisors function (A187793) starting at 15.

%I A274339 #54 Aug 06 2023 15:42:44
%S A274339 15,24,18,15,24,18,15,24,18,15,24,18,15,24,18,15,24,18,15,24,18,15,24,
%T A274339 18,15,24,18,15,24,18,15,24,18,15,24,18,15,24,18,15,24,18,15,24,18,15,
%U A274339 24,18,15,24,18,15,24,18,15,24,18,15,24,18
%N A274339 The period 3 sequence of the iterated sum of deficient divisors function (A187793) starting at 15.
%C A274339 This sequence is generated in a similar way to aliquot sequences or sociable chains, which are generated by iterating the sum of proper divisors function (A001065). It appears to be the only one of period (order, length) 3 that A187793 generates under iteration.
%C A274339 If sigma(N) is the sum of positive divisors of N, then:
%C A274339   a(n+1) = sigma(a(n)) if a(n) is a deficient number (A005100),
%C A274339   a(n+1) = sigma(a(n))-a(n) if a(n) is a primitive abundant number (A071395),
%C A274339   a(n+1) = sigma(a(n))-a(n)-m if a(n) is an abundant number with one proper divisor m that is either perfect (A275082) or abundant, and so forth.
%C A274339 This is used in the example below.
%C A274339 A284326 also generates this sequence under iteration. - _Timothy L. Tiffin_, Feb 22 2022
%H A274339 Colin Barker, <a href="/A274339/b274339.txt">Table of n, a(n) for n = 1..1000</a>
%H A274339 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%F A274339 a(n+3) = a(n).
%F A274339 G.f.: 3*x*(5 + 8*x + 6*x^2) / ((1 - x)*(1 + x + x^2)). - _Colin Barker_, Jan 30 2020
%e A274339 a(1) = 15;
%e A274339 a(2) = sigma(15) = 24;
%e A274339 a(3) = sigma(24) - 24 - 12 - 6 = 18;
%e A274339 a(4) = sigma(18) - 18 - 6 = 15 = a(1).
%t A274339 LinearRecurrence[{0,0,1},{15,24,18},90] (* or *) PadRight[{},90,{15,24,18}] (* _Harvey P. Dale_, Aug 06 2023 *)
%o A274339 (PARI) Vec(3*x*(5 + 8*x + 6*x^2) / ((1 - x)*(1 + x + x^2)) + O(x^40)) \\ _Colin Barker_, Jan 30 2020
%Y A274339 Cf. A001065, A005100, A005101, A071395, A125310, A187793, A274338, A274340, A274380, A274549, A275082, A284326.
%K A274339 nonn,easy
%O A274339 1,1
%A A274339 _Timothy L. Tiffin_, Jun 22 2016