(Translated by https://www.hiragana.jp/)
A349223 - OEIS
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A349223
Numbers k with a record number of ways to factor k into composite factors.
1
1, 4, 16, 36, 64, 96, 144, 240, 288, 360, 432, 480, 576, 720, 864, 960, 1152, 1440, 2160, 2880, 4320, 5040, 5760, 7200, 8640, 10080, 11520, 12960, 14400, 15120, 17280, 20160, 25920, 28800, 30240, 34560, 40320, 50400, 51840, 60480, 80640, 86400, 90720, 100800, 120960
OFFSET
1,2
COMMENTS
Except for the term 4, the indices of records of A050370.
The corresponding record values are 0, 1, 2, 3, 4, 5, 8, 9, 11, 12, 13, 14, ... (see the link for more values).
EXAMPLE
a(1) = 1 since 1 has 0 ways to be factored into composite factors.
a(2) = 4 since 4 is composite and has 1 presentation as a product of composite numbers: 4.
a(3) = 16 since 16 has 2 presentations as a product of composite numbers: 4 * 4 and 16.
a(4) = 36 since 36 has 3 presentations as a product of composite numbers: 6 * 6, 4 * 9 and 36.
MATHEMATICA
f[_, 1] = f[1, _] = 1; f[n_, m_] := f[n, m] = DivisorSum[n, f[n/#, #] &, 1 < # <= m &]; g[n_] := DivisorSum[n, MoebiusMu[n/#]*f[#, #] &]; gm = 0; seq = {1}; Do[g1 = g[n]; If[g1 > gm, gm = g1; AppendTo[seq, n]], {n, 2, 10^5}]; seq
CROSSREFS
Subsequence of A025487.
Sequence in context: A044065 A281795 A063540 * A055808 A016742 A221285
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 11 2021
STATUS
approved