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A153024
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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.
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2
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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
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OFFSET
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1,4
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COMMENTS
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Previous name was: The number of iterations for A153023 to converge when started at n.
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LINKS
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EXAMPLE
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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
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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)))))))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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Andrew Carter (acarter09(AT)newarka.edu), Dec 16 2008
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EXTENSIONS
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STATUS
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approved
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