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
Jinyuan Wang, Table of n, a(n) for n = 1..275
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.
PROG
(Python)
from sympy import divisor_sigma as sigma
def aliquot(n):
alst = []; seen = set(); i = n
while i and i not in seen: alst.append(i); seen.add(i); i = sigma(i) - i
return alst
def aupton(terms): return [max(aliquot(n)) for n in range(1, terms+1)]
print(aupton(66)) # Michael S. Branicky, Jul 11 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Sergio Pimentel, Mar 06 2006
EXTENSIONS
More terms from Jinyuan Wang, Jul 11 2021
STATUS
approved