A115060 Maximum peak of aliquot sequence starting at n.

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

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

Cf. A003023, A005114, A007906, A037020, A044050, A063769, A098007, A098008, A098009, A098010.

Sequence in context: A177872 A271839 A290144 * A004840 A254650 A032994

Adjacent sequences: A115057 A115058 A115059 * A115061 A115062 A115063

Keyword

nonn

Author

Sergio Pimentel, Mar 06 2006

Extensions

More terms from Jinyuan Wang, Jul 11 2021

Status

approved