The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A081699 k-tuple abundance record-holders. 4
 12, 24, 30, 120, 138, 858, 966, 1134, 1218, 1476, 2514, 4494 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A number n is k-tuply abundant if it is abundant and either k = 1 or s(n) is (k-1)-tuply abundant. Thus 24 is doubly abundant: its aliquot chain is 24->36->55->17->1. a(n+1) is defined as the smallest number that is more k-tuply abundant than a(n). 966 is 179-tuply abundant. Lenstra shows that for any k, there is a k-tuply abundant number. Hence the sequence is infinite if and only if the Catalan-Dickson conjecture holds: for all n, the aliquot sequence n, s(n), s(s(n)), ... either terminates at 0 or is periodic. - Charles R Greathouse IV, Jun 28 2021 LINKS H. W. Lenstra, Problem 6064, Amer. Math. Monthly 82 (1975), p. 1016. Solution by the proposer in Amer. Math. Monthly 84 (1977), p. 580. EXAMPLE a(1) = 12 because 12 is the first abundant number. a(3) = 30 because 30 is the first number more k-tuply abundant than a(2). CROSSREFS Cf. A081700, A081705. Sequence in context: A328632 A261435 A103590 * A120570 A164014 A336772 Adjacent sequences:  A081696 A081697 A081698 * A081700 A081701 A081702 KEYWORD nonn,hard,more AUTHOR Gabriel Cunningham (gcasey(AT)mit.edu), Apr 02 2003 EXTENSIONS a(8)-a(12) from David Wasserman, Jun 16 2004 STATUS approved

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

Last modified May 25 18:25 EDT 2022. Contains 354071 sequences. (Running on oeis4.)