OFFSET
1,1
COMMENTS
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.
If sigma(N) is the sum of positive divisors of N, then:
a(n+1) = sigma(a(n)) if a(n) is a deficient number (A005100),
a(n+1) = sigma(a(n))-a(n) if a(n) is a primitive abundant number (A071395),
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.
This is used in the example below.
A284326 also generates this sequence under iteration. - Timothy L. Tiffin, Feb 22 2022
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,1).
FORMULA
a(n+3) = a(n).
G.f.: 3*x*(5 + 8*x + 6*x^2) / ((1 - x)*(1 + x + x^2)). - Colin Barker, Jan 30 2020
EXAMPLE
a(1) = 15;
a(2) = sigma(15) = 24;
a(3) = sigma(24) - 24 - 12 - 6 = 18;
a(4) = sigma(18) - 18 - 6 = 15 = a(1).
MATHEMATICA
LinearRecurrence[{0, 0, 1}, {15, 24, 18}, 90] (* or *) PadRight[{}, 90, {15, 24, 18}] (* Harvey P. Dale, Aug 06 2023 *)
PROG
(PARI) Vec(3*x*(5 + 8*x + 6*x^2) / ((1 - x)*(1 + x + x^2)) + O(x^40)) \\ Colin Barker, Jan 30 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Timothy L. Tiffin, Jun 22 2016
STATUS
approved