A153024 a(n) is the number of iterations of the map k -> A048050(k) to reach zero. If we never reach 0, then a(n) = -1. A048050 gives the sum of proper divisors of k, excluding both 1 and n from the sum.
1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 5, 1, 3, 4, 4, 1, 5, 1, 4, 3, 2, 1, 7, 2, 5, 6, 7, 1, 2, 1, 3, 4, 2, 6, 8, 1, 4, 5, 3, 1, 2, 1, 6, 4, 3, 1, -1, 2, 3, 5, 5, 1, 7, 5, 5, 3, 2, 1, 2, 1, 5, 4, 6, 6, 7, 1, 4, 6, 2, 1, 6, 1, 6, -1, 5, 6, 2, 1, 7, 6, 2, 1, 2, 3, 5, 4, 6, 1, 9, 5, -1, 3, 3, 8, 10, 1, 7, 6, 5, 1, 2, 1, 7, 6
Offset: 1
Keywords
Examples
With m(n) = A048050(n) we have: m(18) -> m(20) -> m(21) -> m(10) -> m(7) -> 0, thus a(18) = 5. On the other hand, m(48) = 75 and m(75) = 48, so we ended in a cycle, thus a(48) = a(75) = -1. - Edited by _Antti Karttunen_, Nov 03 2017
Links
- Antti Karttunen, Table of n, a(n) for n = 1..10000
Programs
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Maple
f := proc(n) L := {} ; a := n ; while not isprime(a) do a := A048050(a) ; if a in L then RETURN(-1) ; fi; L := L union {a} ; od; 1+nops(L) ; end: A153023 := proc(n) if n =1 then 1; elif isprime(n) then 1; else f(n) ; fi; end: # R. J. Mathar, May 25 2013 -
Mathematica
With[{nn = 100}, Table[If[! CompositeQ[n], 1, Length@ NestWhileList[DivisorSigma[1, #] - (# + 1) &, n, Nor[PrimeQ@ #, # == 0] &, 1, 100]] /. k_ /; k == nn + 1 -> -1, {n, 104}]] (* Michael De Vlieger, Nov 03 2017 *) -
Scheme
(define (A153024 n) (let loop ((n n) (visited (list n)) (i 0)) (let ((next (A048050 n))) (cond ((zero? n) i) ((member next visited) -1) (else (loop next (cons next visited) (+ 1 i))))))) (define (A048050 n) (if (= 1 n) 0 (- (A001065 n) 1))) (define (A001065 n) (- (A000203 n) n)) ;; For an implementation of A000203, see under that entry. ;; Antti Karttunen, Nov 03 2017
Extensions
Name changed and more terms added by Antti Karttunen, Nov 03 2017
Comments