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A370789
Ore numbers whose nontrivial divisors are not Ore numbers.
0
6, 28, 496, 6200, 8128, 33550336, 8589869056, 137438691328
OFFSET
1,1
COMMENTS
It seems this is a supersequence of A000396 (confirmed for all available terms of A000396).
EXAMPLE
The nontrivial divisors of 6 are 2 and 3 that do not belong to A001599, so 6 is a term.
No nontrivial divisor of 6200 is a term of A001599, which makes 6200 a term of the present sequence. On the other hand, 6200 is not a perfect number.
MATHEMATICA
oreQ[n_] := IntegerQ[n*DivisorSigma[0, n]/DivisorSigma[1, n]];
ntdNotOreQ[n_] := NoneTrue[Most[Rest[Divisors[n]]], oreQ[#] &];
a001599 = Cases[Import["https://oeis.org/A001599/b001599.txt", "Table"],
{_, _}][[All, 2]];
Select[Rest[a001599], ntdNotOreQ[#] &]
CROSSREFS
Sequence in context: A326145 A174633 A345004 * A351440 A325637 A336702
KEYWORD
nonn,more
AUTHOR
Ivan N. Ianakiev, Mar 02 2024
STATUS
approved