

A334814


Least number that reaches 1 after n iterations of the map k > sigma(k)/d(k) if d(k)  sigma(k), and k > 1 otherwise, where d(k) is the number of divisors of k (A000005) and sigma(k) is their sum (A000203).


0



1, 2, 3, 5, 11, 29, 107, 257, 941, 2017, 11261, 45039, 441073, 2151073, 8575873, 42884161, 220268161, 440536321
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OFFSET

0,2


COMMENTS

Apparently, most of the terms are primes. 45039 = 3 * 15013 is the first composite term.
a(18) > 2*10^10, if it exists.


LINKS



EXAMPLE

a(3) = 5 since sigma(5)/d(5) = 6/2 = 3, sigma(3)/d(3) = 4/2 = 2, and sigma(2)/d(2) = 3/2 is not an integer, hence there are 3 iterations: 5 > 3 > 2 > 1, and 5 is the least number with 3 iterations.


MATHEMATICA

rat[n_] := If[IntegerQ[r = DivisorSigma[1, n]/DivisorSigma[0, n]], r, 1]; f[n_] := Length @ FixedPointList[rat, n]  1; max = 10; seq = Table[0, {max}]; c = 0; n = 1; While[c < max, i = f[n]; If[i <= max && seq[[i]] == 0, c++; seq[[i]] = n]; n++]; seq


CROSSREFS



KEYWORD

nonn,more


AUTHOR



STATUS

approved



