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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 (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

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

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Last modified December 2 13:15 EST 2021. Contains 349444 sequences. (Running on oeis4.)