A370789 Ore numbers whose nontrivial divisors are not Ore numbers.

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).

Assuming odd perfect numbers do not exist, the above conjecture is true since: a) an even perfect number is not divisible by a smaller even perfect number, b) an even perfect number is not divisible by a smaller nonperfect Ore number k with omega(k)>=3, and c) all Ore numbers m with omega(m)=2 are even perfect numbers (see Carl Pomerance link at A001599). - Ivan N. Ianakiev, Apr 14 2025

Is 6200 the only term that is not a perfect number? - Ivan N. Ianakiev, Apr 04 2025

Links

Table of n, a(n) for n=1..8.

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

Cf. A000396, A001599.

Sequence in context: A326145 A174633 A345004 * A351440 A379491 A325637

Adjacent sequences: A370786 A370787 A370788 * A370790 A370791 A370792

Keyword

nonn,more

Author

Ivan N. Ianakiev, Mar 02 2024

Status

approved