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%I #15 Nov 03 2017 09:55:48
%S 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,
%T 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,
%U 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
%N 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.
%C Previous name was: The number of iterations for A153023 to converge when started at n.
%H Antti Karttunen, <a href="/A153024/b153024.txt">Table of n, a(n) for n = 1..10000</a>
%e With m(n) = A048050(n) we have: m(18) -> m(20) -> m(21) -> m(10) -> m(7) -> 0, thus a(18) = 5.
%e 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
%p 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:
%p A153023 := proc(n) if n =1 then 1; elif isprime(n) then 1; else f(n) ; fi; end: # _R. J. Mathar_, May 25 2013
%t 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 *)
%o (Scheme)
%o (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)))))))
%o (define (A048050 n) (if (= 1 n) 0 (- (A001065 n) 1)))
%o (define (A001065 n) (- (A000203 n) n)) ;; For an implementation of A000203, see under that entry.
%o ;; _Antti Karttunen_, Nov 03 2017
%Y Cf. A048050, A153023.
%K sign
%O 1,4
%A Andrew Carter (acarter09(AT)newarka.edu), Dec 16 2008
%E Name changed and more terms added by _Antti Karttunen_, Nov 03 2017
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