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A225353
Numbers having no partition into distinct squarefree divisors.
4
4, 8, 9, 16, 18, 20, 24, 25, 27, 28, 32, 36, 40, 44, 45, 48, 49, 50, 52, 54, 56, 63, 64, 68, 72, 75, 76, 80, 81, 88, 90, 92, 96, 98, 99, 100, 104, 108, 112, 116, 117, 120, 121, 124, 125, 126, 128, 135, 136, 140, 144, 147, 148, 150, 152, 153, 160, 162, 164
OFFSET
1,1
COMMENTS
A225245(a(n)) = 0.
Verified up to a(366) = 1000, a(n) is also the order of a finite group G for which |Out(G)|>|G| for at least one group of order a(n), Out(G) being the outer automorphism group of G. - Miles Englezou, Apr 19 2024
By definition, a(n) is nonsquarefree for every n, since every squarefree number m has a trivial partition into distinct squarefree divisors m = m. - Miles Englezou, Apr 20 2024
If k is a term then so is k*m where m|k. - David A. Corneth, Apr 27 2024
LINKS
MATHEMATICA
f[n_] := Coefficient[Product[If[MoebiusMu[d] != 0, 1 + x^d, 1], {d, Divisors[n]}], x, n];
Select[Range[200], f[#] == 0&] (* Jean-François Alcover, May 04 2024, after Ilya Gutkovskiy in A225245 *)
PROG
(Haskell)
import Data.List (elemIndices)
a225353 n = a225353_list !! (n-1)
a225353_list = map (+ 1) $ elemIndices 0 a225245_list
CROSSREFS
Cf. A013929, A225245, A225354 (complement).
Sequence in context: A242663 A160053 A140612 * A034023 A086368 A034024
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, May 05 2013
STATUS
approved