

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
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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).
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.


KEYWORD

nonn,easy


AUTHOR



STATUS

approved



