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A045782 Number of factorizations of n for some n (range of A001055). 3

%I

%S 1,2,3,4,5,7,9,11,12,15,16,19,21,22,26,29,30,31,36,38,42,45,47,52,56,

%T 57,64,66,67,74,77,92,97,98,101,105,109,118,135,137,139,141,162,165,

%U 171,176,181,189,195,198,203,212,231,249,250,254,257,267,269,272,289

%N Number of factorizations of n for some n (range of A001055).

%H Florian Luca, Anirban Mukhopadhyay and Kotyada Srinivas, <a href="http://arxiv.org/abs/0807.0986">On the Oppenheim's "factorisatio numerorum" function</a>, arXiv:0807.0986 [math.NT], 2008.

%F The Luca et al. paper shows that the number of terms with a(n) <= x is x^{ O( log log log x / log log x )}. - _N. J. A. Sloane_, Jun 12 2009

%t terms = 61; m0 = 10^5; dm = 10^4;

%t f[1, _] = 1; f[n_, k_] := f[n, k] = Sum[f[n/d, d], {d, Select[Divisors[n], 1 < # <= k &]}];

%t Clear[seq]; seq[m_] := seq[m] = Sort[Tally[Table[f[n, n], {n, 1, m}]][[All, 1]]][[1 ;; terms]]; seq[m = m0]; seq[m += dm]; While[Print[m]; seq[m] != seq[m - dm], m += dm];

%t seq[m] (* _Jean-Fran├žois Alcover_, Oct 04 2018 *)

%Y Cf. A001055, A045783.

%K nonn

%O 1,2

%A _David W. Wilson_

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Last modified September 18 07:50 EDT 2019. Contains 327168 sequences. (Running on oeis4.)