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A045782 Number of factorizations of n for some n (range of A001055). 3
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, 57, 64, 66, 67, 74, 77, 92, 97, 98, 101, 105, 109, 118, 135, 137, 139, 141, 162, 165, 171, 176, 181, 189, 195, 198, 203, 212, 231, 249, 250, 254, 257, 267, 269, 272, 289 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..61.

Florian Luca, Anirban Mukhopadhyay and Kotyada Srinivas, On the Oppenheim's "factorisatio numerorum" function, arXiv:0807.0986 [math.NT], 2008.

FORMULA

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

MATHEMATICA

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

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

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];

seq[m] (* Jean-Fran├žois Alcover, Oct 04 2018 *)

CROSSREFS

Cf. A001055, A045783.

Sequence in context: A258456 A230843 A188551 * A184112 A064005 A306587

Adjacent sequences:  A045779 A045780 A045781 * A045783 A045784 A045785

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified August 25 05:45 EDT 2019. Contains 326323 sequences. (Running on oeis4.)