A326726 The prime factorization of abs(E(2k)) for k >= 2, E(k) the k-th Euler number. Factors sorted by size with the smallest factor negated. a(n) = -1 by convention for n = 1, 2.

-1, -1, -5, -61, -5, 277, -19, 2659, -5, 13, 43, 967, -47, 4241723, -5, 17, 228135437, -79, 349, 87224971, -5, 5, 41737, 354957173, -31, 1567103, 1427513357, -5, 13, 2137, 111691689741601, -67, 61001082228255580483, -5, 19, 29, 71, 30211, 2717447, 77980901

Offset

1,3

Comments

For small Euler numbers the factorizations were computed with SageMath, see the b-file for the script. For larger Euler numbers the values were taken from the table of S. S. Wagstaff, Jr..

The smallest factor was negated only to be able to distinguish the individual factorizations easily. (No general formula for the number of factors is known.)

The factorizations listed in the b-file currently go up to E(164) (the prime factors of E(166) are not yet known).

Links

Peter Luschny, Table of n, a(n) for n = 1..428

factordb, Status of E(166).

S. S. Wagstaff, Prime factors of the absolute values of Euler numbers

Example

The data is given as a flatted list of factorizations written with the conventions
stated above. Because it is a list the offset is 1. The list starts:
[[-1], [-1], [-5], [-61], [-5, 277], [-19, 2659], [-5, 13, 43, 967], [-47, 4241723], [-5, 17, 228135437], [-79, 349, 87224971], [-5, 5, 41737, 354957173], ... ].
The first few factorizations are:
E(4)  = 5;
E(6)  = 61;
E(8)  = 5 * 277;
E(10) = 19 * 2659;
E(12) = 5 * 13 * 43 * 967;
E(14) = 47 * 4241723;
E(16) = 5 * 17 * 228135437;
E(18) = 79 * 349 * 87224971;
E(20) = 5 * 5 * 41737 * 354957173;
E(22) = 31 * 1567103 * 1427513357;
E(24) = 5 * 13 * 2137 * 111691689741601;

Prog

(Sage) # See b-file.

Crossrefs

Cf. A122045, A000364, A326727.

Sequence in context: A350360 A293454 A162129 * A367337 A141967 A139915

Adjacent sequences: A326723 A326724 A326725 * A326727 A326728 A326729

Keyword

sign,tabf,hard

Author

Peter Luschny, Jul 29 2019

Status

approved