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a(n) is the least number whose aliquot sequence begins with exactly n weird numbers (A006037), or -1 if no such numbers exists.
1

%I #6 Apr 16 2024 14:03:31

%S 1,70,97930,597730,77420770,459940810,11835050710

%N a(n) is the least number whose aliquot sequence begins with exactly n weird numbers (A006037), or -1 if no such numbers exists.

%C a(7) > 10^11, if it exists.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Aliquot_sequence">Aliquot sequence</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Weird_number">Weird number</a>.

%e The iterations of A001065 over the terms a(1)..a(6):

%e n | a(n) | Iterations

%e --+-------------+--------------------------------------------------------------

%e 1 | 70 | 70

%e 2 | 97930 | 97930 -> 103670

%e 3 | 597730 | 597730 -> 632030 -> 668290

%e 4 | 77420770 | 77420770 -> 82246430 -> 86946370 -> 92477630

%e 5 | 459940810 | 459940810 -> 487175990 -> 515884810 -> 546184310 -> 582130570

%e 6 | 11835050710 | 11835050710 -> 12515648810 -> 13235404630 -> 13991713610

%e | | -> 14797250230 -> 15649107530

%Y Cf. A001065, A006037, A371950.

%K nonn,hard,more

%O 0,2

%A _Amiram Eldar_, Apr 14 2024