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A274340 A 4-cycle of the iterated sum of deficient divisors function. 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 cycle is generated in a similar way to the aliquot sequences (or sociable chains) that are generated by the sum of proper divisors function.  This cycle appears to be one of just two cycles of length (or order) 4 that are generated by the sum of deficient divisors function.

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, a(n+1) = sigma(a(n))-a(n) if a(n) is a primitive abundant number, a(n+1) = sigma(a(n))-a(n)-m if a(n) is an abundant number with one proper divisor m that is either abundant or perfect, and so forth.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

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), ...

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

Cf. A125310, A187793, A274338, A274339, A274380, A274549.

Sequence in context: A093680 A007640 A265201 * A241849 A054304 A151979

Adjacent sequences:  A274337 A274338 A274339 * A274341 A274342 A274343

KEYWORD

nonn,easy

AUTHOR

Timothy L. Tiffin, Jun 22 2016

STATUS

approved

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Last modified July 27 20:33 EDT 2021. Contains 346308 sequences. (Running on oeis4.)