

A115060


Maximum peak of aliquot sequence starting at n.


4



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 13, 14, 15, 16, 17, 21, 19, 22, 21, 22, 23, 55, 25, 26, 27, 28, 29, 259, 31, 32, 33, 34, 35, 55, 37, 38, 39, 50, 41, 259, 43, 50, 45, 46, 47, 76, 49, 50, 51, 52, 53, 259, 55, 64, 57, 58, 59, 172
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

According to Catalan's conjecture all aliquot sequences end in a prime followed by 1, a perfect number, a friendly pair or an aliquot cycle. Some sequences seem to be open ended and keep growing forever i.e. 276. Most sequences only go down (i.e. 10  8  7  1), so for most cases in this sequence, a(n) = n. The first number to achieve a significantly high peak is 138


LINKS

Table of n, a(n) for n=1..60.
W. Creyaufmueller, Aliquot Sequences.
Paul Zimmerman, Aliquot Sequences.


EXAMPLE

a(24)=55 because the aliquot sequence starting at 24 is: 24  36  55  17  1 so the maximum peak of this sequence is 55.


CROSSREFS

Cf. A098007, A003023, A098008, A098009, A098010, A044050, A007906, A037020, A063769, A005114.
Sequence in context: A177872 A271839 A290144 * A004840 A254650 A032994
Adjacent sequences: A115057 A115058 A115059 * A115061 A115062 A115063


KEYWORD

nonn,more


AUTHOR

Sergio Pimentel, Mar 06 2006


STATUS

approved



