A327159 Size of the cycle containing n in the map x -> usigma(x)-x or 0 if n is not a member of any finite cycle. Here usigma is the sum of unitary divisors of n (A034448).

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0

Offset

1,30

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Example

Because A034460(6) = 6, a(6) = 1.
Because A034460(30) = 42, A034460(42) = 54, A034460(54) = 30, a(30) = a(42) = a(54) = 3.
Because A034460(90) = 90, a(90) = 1. Because A034460(78) = 90, a(78) = 0, as even though 78 ends into a cycle of one, it itself is not a part of that cycle.

Mathematica

a034460[0] = 0; (* avoids dividing by 0 when an iteration reaches 0 *)
a034460[n_] := Total[Select[Divisors[n], GCD[#, n/#] == 1 &]] - n /; n > 0
cycleL[k_] := Module[{nL=NestWhileList[a034460, k, UnsameQ, All]}, If[k==Last[nL], Length[nL]-1, 0]]
a327159[n_] := Map[cycleL, Range[n]]
a327159[120] (* Hartmut F. W. Hoft, Feb 04 2024 *)

Prog

(PARI)
A034460(n) = (sumdivmult(n, d, if(gcd(d, n/d)==1, d))-n); \\ From A034460
A327159(n, orgn=n, xs=Set([])) = if(1==n, 0, if(vecsearch(xs, n), if(n==orgn, length(xs), 0), xs = setunion([n], xs); A327159(A034460(n), orgn, xs)));

Crossrefs

Cf. A002827 (positions of ones), A063991 (of 2's), A319902 (of 4's), A097024 (of 5's), A319917 (of 6's), A319937 (of 10's), A097030 (of 14's), A327157 (of all nonzero terms).

Cf. also A034448, A034460, A097031, A318880, A318882, A327162.

Sequence in context: A061853 A010104 A282673 * A373695 A280051 A030121

Adjacent sequences: A327156 A327157 A327158 * A327160 A327161 A327162

Keyword

nonn

Author

Antti Karttunen, Aug 28 2019

Status

approved