cp's OEIS Frontend

A274340 The period 4 sequence of the iterated sum of deficient divisors function (A187793) starting at 19.

%I A274340 #51 Oct 16 2023 16:13:27
%S A274340 19,20,22,36,19,20,22,36,19,20,22,36,19,20,22,36,19,20,22,36,19,20,22,
%T A274340 36,19,20,22,36,19,20,22,36,19,20,22,36,19,20,22,36,19,20,22,36,19,20,
%U A274340 22,36,19,20,22,36,19,20,22,36,19,20,22,36
%N A274340 The period 4 sequence of the iterated sum of deficient divisors function (A187793) starting at 19.
%C A274340 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 one of two sequences of period (order, length) 4 that A187793 generates under iteration. The other one is A274380.
%C A274340 If sigma(N) is the sum of positive divisors of N, then:
%C A274340   a(n+1) = sigma(a(n)) if a(n) is a deficient number (A005100),
%C A274340   a(n+1) = sigma(a(n))-a(n) if a(n) is a primitive abundant number (A071395),
%C A274340   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 A274340 This is used in the example below.
%H A274340 Colin Barker, <a href="/A274340/b274340.txt">Table of n, a(n) for n = 1..1000</a>
%H A274340 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).
%F A274340 a(n+4) = a(n).
%F A274340 a(n) = A187793(a(n-1)).
%F A274340 G.f.: x*(19 + 20*x + 22*x^2 + 36*x^3) / (1 - x^4). - _Colin Barker_, Jan 30 2020
%e A274340 a(1) = 19;
%e A274340 a(2) = sigma(19) = 20;
%e A274340 a(3) = sigma(20) - 20 = 22;
%e A274340 a(4) = sigma(22) = 36;
%e A274340 a(5) = sigma(36) - 36 - 18 - 12 - 6 = 19 = a(1).
%t A274340 PadRight[{},100,{19,20,22,36}] (* _Paolo Xausa_, Oct 16 2023 *)
%o A274340 (PARI) Vec(x*(19 + 20*x + 22*x^2 + 36*x^3) / (1 - x^4) + O(x^80)) \\ _Colin Barker_, Jan 30 2020
%Y A274340 Cf. A001065, A005100, A005101, A071395, A125310, A187793, A274338, A274339, A274380, A274549, A275082.
%K A274340 nonn,easy
%O A274340 1,1
%A A274340 _Timothy L. Tiffin_, Jun 22 2016