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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Previous name was: The number of iterations for A153023 to converge when started at n.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

EXAMPLE

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

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 *)

PROG

(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

CROSSREFS

Cf. A048050, A153023.

Sequence in context: A112971 A299201 A050379 * A066921 A076649 A157235

Adjacent sequences:  A153021 A153022 A153023 * A153025 A153026 A153027

KEYWORD

sign

AUTHOR

Andrew Carter (acarter09(AT)newarka.edu), Dec 16 2008

EXTENSIONS

Name changed and more terms added by Antti Karttunen, Nov 03 2017

STATUS

approved

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Last modified February 19 19:21 EST 2020. Contains 332047 sequences. (Running on oeis4.)