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

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

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

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).

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

Cf. A001065, A005100, A005101, A071395, A125310, A187793, A274338, A274339, A274380, A274549, A275082.

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