The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A323328 Lexicographically earliest unbounded aliquot-like sequence based on the Dedekind psi function: a(1) = 318, a(n) = t(a(n-1)) where t(k) = A001615(k) - k. 6

%I #10 Mar 15 2024 18:43:43

%S 318,330,534,546,798,1122,1470,2562,3390,4818,5838,7602,9870,17778,

%T 17790,24978,27438,30882,30894,34386,40782,52530,82254,82266,82278,

%U 106074,111654,111690,176022,266346,266382,266490,480006,480330,674406,740826,833814,834138

%N Lexicographically earliest unbounded aliquot-like sequence based on the Dedekind psi function: a(1) = 318, a(n) = t(a(n-1)) where t(k) = A001615(k) - k.

%C 318 is the least number k whose repeated iteration of the mapping k -> A001615(k) - k yields an unbounded sequence. Since t(m^j * n) = m^j * t(n) if m|n, then if in the sequence a_0 = k, a_1 = t(k), a_2 = t(t(k))... there is a term a_{i1} = m^j * a_0 such that m|k and j > 0 then a_{i+i1} = m^j * a_i for all i and thus the sequence is unbounded. Since a(13)=9870, after 19 iterations a(32) = 27 * 9870, 27 = 3^3 and 3|9870 then a(n+19) = 27 * a(n) for n >= 13.

%D Jean-Marie De Koninck, Those Fascinating Numbers, Amer. Math. Soc., 2009, page 71, entry 318.

%H Amiram Eldar, <a href="/A323328/b323328.txt">Table of n, a(n) for n = 1..10000</a>

%H Kevin Brown and Charles Vanden Eynden, <a href="https://www.jstor.org/stable/2974888">Pseudo-aliquot Sequences, Solution to Problem 10323</a>, The American Mathematical Monthly, Volume 103, No. 8 (1996), pp. 697-698.

%H David E. Penney and Carl Pomerance, <a href="https://www.jstor.org/stable/10.2307/2323896">Problem 10323</a>, The American Mathematical Monthly, Volume 100, No. 7 (1993), p. 688.

%t t[1] = 0; t[n_] := (Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]) - 1)*n; NestList[t, 318, 40]

%Y Cf. A001615, A008892, A323327.

%K nonn

%O 1,1

%A _Amiram Eldar_, Jan 11 2019

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)