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A319238
Positions of zeros in A114592, the list of coefficients in the expansion of Product_{n > 1} (1 - 1/n^s).
9
6, 8, 10, 14, 15, 16, 21, 22, 26, 27, 33, 34, 35, 38, 39, 46, 51, 55, 57, 58, 62, 64, 65, 69, 74, 77, 81, 82, 85, 86, 87, 91, 93, 94, 95, 96, 106, 111, 115, 118, 119, 120, 122, 123, 125, 129, 133, 134, 141, 142, 143, 144, 145, 146, 155, 158, 159, 160, 161, 166
OFFSET
1,1
COMMENTS
From Tian Vlasic, Jan 01 2022: (Start)
Numbers that have an equal number of even- and odd-length unordered factorizations into distinct factors.
For prime p, by the pentagonal number theorem, p^k is a term if and only if k is in A090864.
For primes p and q, p*q^k is a term if and only if k = A000326(m)+N with 0 <= N < m. (End)
LINKS
EXAMPLE
16 = 2*8 = 4*4 = 2*2*4 = 2*2*2*2 has an equal number of even-length factorizations and odd-length factorizations into distinct factors (1). - Tian Vlasic, Dec 31 2021
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Join@@Position[Table[Sum[(-1)^Length[f], {f, Select[facs[n], UnsameQ@@#&]}], {n, 100}], 0]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 15 2018
STATUS
approved