A199969 a(n) = the greatest non-divisor h of n (1 < h < n), or 0 if no such h exists.

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

Offset: 1

Author

Jaroslav Krizek, Nov 26 2011

Keywords

• nonn
• easy
• less

Comments

From Paul Curtz, Feb 09 2015: (Start)

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

• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A199968 (the smallest non-divisor h of n (1A199970. A001477, A011973, A034807, A054977, A254667.

Cf. A007978.

Essentially the same as A000027, A028310, A087156 etc.

Programs

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 *)

PARI

if(n>2,n-1,0) \\ Charles R Greathouse IV, Sep 02 2015

Formula

a(n) = n-1 for n >= 3.

E.g.f.: 1-x^2/2+(x-1)*exp(x). - Enrique Navarrete, May 11 2021