|
|
A199969
|
|
a(n) = the greatest non-divisor h of n (1 < h < n), or 0 if no such h exists.
|
|
8
|
|
|
0, 0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
The nonnegative numbers with 0 instead of 1. See A254667(n), which is linked to the Bernoulli numbers A164555(n)/A027642(n), an autosequence of the second kind.
Offset 0 could be chosen.
An autosequence of the second kind is a sequence whose main diagonal is the first upper diagonal multiplied by 2. If the first upper diagonal is
s0, s1, s2, s3, s4, s5, ...,
the sequence is
Ssk(n) = 2*s0, s0, s0 + 2*s1, s0 +3*s1, s0 + 4*s1 + 2*s2, s1 + 5*s1 + 5*s2, etc.
The corresponding coefficients are A034807(n), a companion to A011973(n).
The binomial transform of Ssk(n) is (-1)^n*Ssk(n).
Difference table of a(n):
0, 0, 2, 3, 4, 5, 6, 7, ...
0, 2, 1, 1, 1, 1, 1, ...
2, -1, 0, 0, 0, 0 ...
-3, 1, 0, 0, 0, ...
4, -1, 0, 0, ...
-5, 1, 0, ...
6, -1, ...
7, ...
etc.
a(n) is an autosequence of the second kind. See A054977(n).
The corresponding autosequence of the first kind (a companion) is 0, 0 followed by the nonnegative numbers (A001477(n)). Not in the OEIS.
Ssk(n) = 2*Sfk(n+1) - Sfk(n) where Sfk(n) is the corresponding sequence of the first kind (see A254667(n)).
(End)
Number of binary sequences of length n-1 that contain exactly one 0 and at least one 1. - Enrique Navarrete, May 11 2021
|
|
LINKS
|
|
|
FORMULA
|
a(n) = n-1 for n >= 3.
|
|
MATHEMATICA
|
Join[{0, 0}, Table[Max[Complement[Range[n], Divisors[n]]], {n, 3, 70}]] (* or *) Join[{0, 0}, Range[2, 70]] (* Harvey P. Dale, May 31 2014 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,less
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|