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 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 (list; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=0..17. 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 Cf. A000005, A000203, A003601, A102187, A330816, A334813. Sequence in context: A190197 A173631 A182987 * A364802 A360815 A087580 Adjacent sequences: A334811 A334812 A334813 * A334815 A334816 A334817 KEYWORD nonn,more AUTHOR Amiram Eldar, May 12 2020 STATUS approved

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Last modified July 13 04:46 EDT 2024. Contains 374267 sequences. (Running on oeis4.)