A368459 Numbers k such that 2*(Bacher(k) - sigma(k)) + k + 1 < 0.

6, 8, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95

Offset: 1

Author

Peter Luschny, Dec 26 2023

Keywords

• nonn

Comments

Complementary to A368458, this sequence lists the indices of negative values of A368457. See the comments in A368458.

In summary, A368458 U A368459 U Primes U {35, ...} decomposes the positive integers into disjoint sets, whereby the nature of the fourth set is currently unclear; probably, it has only 35 as a member.

Links

• Roland Bacher, A quixotic proof of Fermat's two squares theorem for prime numbers, American Mathematical Monthly, Vol. 130, No. 9 (November 2023), 824-836; arXiv version, arXiv:2210.07657 [math.NT], 2022.

Crossrefs

Cf. A000203, A100484, A001248, A368207, A368457, A368458, A368460.

Programs

Julia

println([n for n in 1:95 if A368457(n) < 0])

Formula

k is a term <=> A368457(k) < 0 <=> 2*(A368207(k) - A000203(k)) + k + 1 < 0.