

A274380


A 4cycle of the iterated sum of deficient divisors function.


5



34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48
(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

Table of n, a(n) for n=1..60.


FORMULA

a(n+4) = a(n).


EXAMPLE

a(1) = 34, a(2) = sigma(34) = 54, a(3) = sigma(54)186 = 42, a(4) = sigma(42)426 = 48, a(5) = sigma(48)4824126 = 34 = a(1), ...


CROSSREFS

Cf. A125310, A187793, A274338, A274339, A274340, A274549.
Sequence in context: A092888 A217768 A217704 * A305061 A051969 A241520
Adjacent sequences: A274377 A274378 A274379 * A274381 A274382 A274383


KEYWORD

nonn,easy


AUTHOR

Timothy L. Tiffin, Jun 22 2016


STATUS

approved



