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

1,4

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: A342085 A050379 A344589 * 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