|
|
A342320
|
|
Integers k such that Euler(k, 1) is an integer multiple of Bernoulli(k + 1, 1).
|
|
3
|
|
|
0, 1, 5, 17, 41, 53, 125, 161, 293, 341, 377, 485, 881, 1025, 1133, 1313, 1457, 1805, 2057, 2393, 2645, 3077, 3401, 3941, 4373, 5333, 5417, 6173, 6497, 7181, 7937, 9197, 9233, 10205, 11825, 12641, 13121, 14153, 14405, 16001, 16253, 16757, 18521, 19493, 21545
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
Numbers k such that k + 1 divides 2^(k + 2) - 2. - Vaclav Kotesovec, Mar 24 2021
|
|
EXAMPLE
|
Let E(n) = Euler(n, 1) and B(n) = Bernoulli(n, 1).
2*E(0) = 4*B(1) = 2;
2*E(1) = 6*B(2) = 1;
2*E(5) = 42*B(6) = 1;
2*E(17) = 58254*B(18) = 3202291;
2*E(41) = 418861572486*B(42) = 352552873457246307069012458671.
|
|
MATHEMATICA
|
Join[{0}, Select[Range[1000], BernoulliB[#+1, 1] != 0 && IntegerQ[EulerE[#, 1]/BernoulliB[#+1, 1]] &]] (* Vaclav Kotesovec, Mar 24 2021 *)
Select[Range[100000], IntegerQ[(2*(-1 + 2^#))/#] & ] - 1 (* Vaclav Kotesovec, Mar 24 2021 *)
L342320 := Select[Range[0, 10000], Divisible[2^(# + 2) - 2, # + 1] &];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|