A097024 - OEIS

A097024

Numbers in the 5-cycle-attractor of the function f(x)=A063919(x).

1482, 1878, 1890, 2142, 2178

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OFFSET

1,1

COMMENTS

A002827 provides 1-cycle terms = unitary perfect numbers.

A063991 gives 2-cycle elements = unitary amicable numbers.

A097030 collects true 14-cycle elements, i.e., terms in end-cycle of length 14 when A063919(x) function is iterated.

Concerning 3-cycle elements, only {30,42,54} were encountered.

LINKS

J. O. M. Pedersen, Order 5 cycles, 2007.

MATHEMATICA

a063919[1] = 1; (* function a[] in A063919 by Jean-François Alcover *)

a063919[n_] := Total[Select[Divisors[n], GCD[#, n/#]==1&]]-n/; n>1

a097024Q[k_] := Module[{a=NestList[a063919, k, 5]}, Count[a, k]==2&&Last[a]==k]

a097024[n_] := Select[Range[n], a097024Q]

a097024[2178] (* Hartmut F. W. Hoft, Jan 24 2024 *)

PROG

(PARI) f(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d)) - n;

isok5(n) = iferr(f(f(f(f(f(n))))) == n, E, 0);

isok1(n) = iferr(f(n) == n, E, 0);

isok(n) = !isok1(n) && isok5(n); \\ Michel Marcus, Sep 28 2018

CROSSREFS

KEYWORD

nonn,more

AUTHOR

Labos Elemer, Aug 30 2004

STATUS

approved