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A274340 The period 4 sequence of the iterated sum of deficient divisors function (A187793) starting at 19. 6
19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36 (list; graph; refs; listen; history; text; internal format)
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 one of two sequences of period (order, length) 4 that A187793 generates under iteration. The other one is A274380.
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.
LINKS
FORMULA
a(n+4) = a(n).
a(n) = A187793(a(n-1)).
G.f.: x*(19 + 20*x + 22*x^2 + 36*x^3) / (1 - x^4). - Colin Barker, Jan 30 2020
EXAMPLE
a(1) = 19;
a(2) = sigma(19) = 20;
a(3) = sigma(20) - 20 = 22;
a(4) = sigma(22) = 36;
a(5) = sigma(36) - 36 - 18 - 12 - 6 = 19 = a(1).
MATHEMATICA
PadRight[{}, 100, {19, 20, 22, 36}] (* Paolo Xausa, Oct 16 2023 *)
PROG
(PARI) Vec(x*(19 + 20*x + 22*x^2 + 36*x^3) / (1 - x^4) + O(x^80)) \\ Colin Barker, Jan 30 2020
CROSSREFS
Sequence in context: A093680 A007640 A265201 * A241849 A054304 A151979
KEYWORD
nonn,easy
AUTHOR
Timothy L. Tiffin, Jun 22 2016
STATUS
approved

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Last modified May 28 21:13 EDT 2024. Contains 372920 sequences. (Running on oeis4.)