The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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