

A323328


Lexicographically earliest unbounded aliquotlike sequence based on the Dedekind psi function: a(1) = 318, a(n) = t(a(n1)) where t(k) = A001615(k)  k.


6



318, 330, 534, 546, 798, 1122, 1470, 2562, 3390, 4818, 5838, 7602, 9870, 17778, 17790, 24978, 27438, 30882, 30894, 34386, 40782, 52530, 82254, 82266, 82278, 106074, 111654, 111690, 176022, 266346, 266382, 266490, 480006, 480330, 674406, 740826, 833814, 834138
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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 mn, 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 mk 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 39870 then a(n+19) = 27 * a(n) for n >= 13.


REFERENCES

JeanMarie De Koninck, Those Fascinating Numbers, Amer. Math. Soc., 2009, page 71, entry 318.


LINKS

David E. Penney and Carl Pomerance, Problem 10323, The American Mathematical Monthly, Volume 100, No. 7 (1993), p. 688.


MATHEMATICA

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


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



