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A115060
Maximum peak of aliquot sequence starting at n.
6
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, 61, 62, 63, 64, 65, 259
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
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
KEYWORD
nonn
AUTHOR
Sergio Pimentel, Mar 06 2006
EXTENSIONS
More terms from Jinyuan Wang, Jul 11 2021
STATUS
approved