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A153023
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If n is 1 or prime then a(n) = n. Otherwise, start with n and iterate the map k -> A048050(k) until we reach a prime p; then a(n) = p. If we never reach a prime, 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, 2, 3, 2, 5, 5, 7, 5, 3, 7, 11, 5, 13, 3, 5, 3, 17, 7, 19, 7, 7, 13, 23, 5, 5, 5, 5, 5, 29, 41, 31, 41, 3, 19, 5, 7, 37, 7, 3, 7, 41, 53, 43, 3, 41, 5, 47, -1, 7, 53, 7, 41, 53, 7, 3, 7, 13, 31, 59, 107, 61, 3, 7, 3, 7, 7, 67, 13, 5, 73, 71, 7, 73, 3, -1, 7, 7, 89, 79, 41, 3, 43, 83, 139, 13
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OFFSET
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1,2
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LINKS
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EXAMPLE
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a(18) -> {2,3,6,9} -> 20 -> {2,4,5,10} -> 21 -> {3,7} -> 10 -> {2,5} -> 7 = 7.
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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; a ; end:
A048050 := proc(n) numtheory[sigma](n)-n-1 ; end:
A153023 := proc(n) if n =1 then 1; elif isprime(n) then n; else f(n) ; fi; end: # R. J. Mathar, Dec 19 2008
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MATHEMATICA
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Table[If[! CompositeQ[n], n, NestWhile[DivisorSigma[1, #] - (# + 1) &, n, Nor[PrimeQ@ #, # == 0] &, 1, 100] /. k_ /; CompositeQ@ k -> -1], {n, 85}] (* Michael De Vlieger, Nov 03 2017 *)
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PROG
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(Scheme)
(define (A153023 n) (let loop ((n n) (visited (list n))) (let ((next (A048050 n))) (cond ((or (= 1 n) (= 1 (A010051 n))) n) ((member next visited) -1) (else (loop next (cons next visited)))))))
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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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