login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A237110 Maximum number of distinct prime factors of pairs of coprime g and h (g < h) adding to n. 1
1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 4, 2, 4, 3, 3, 3, 3, 2, 4, 3, 3, 3, 4, 2, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 2, 4, 3, 3, 3, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 3, 4, 4, 3, 4, 3, 4, 3, 4, 3, 4, 4, 4, 3, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,3
COMMENTS
This sequence is defined for n >= 3.
The difference between this sequence and A237354 is that A237354 allows g and h have common factors while in this sequence g and h must be coprime.
The smallest n that makes a(n)=k gives the sequence A182987, Least a+b such that ab=A002110(n).
The largest n that makes a(n)=k forms a sequence starting with 6, 60, 420, 6930, 30030, which are Prime(2)#, 2*Prime(3)#, 2*Prime(4)#, 3*Prime(5)#, where p# denotes the product of prime numbers up to p.
The largest n that makes a(n)=5 is not found yet; it is greater than Prime(6)#.
LINKS
EXAMPLE
n=3, 3=1+2. 1 has no prime factors. 2 has one. So a(3)=0+1=1;
n=5, 5=1+4=1+2^2, gives number of prime factors 0+1=1, and 5=2+3, gives 1+1=2. So a(5)=2;
...
n=97, 97=1+96=1+2^5*3, gives number of distinct prime factors of g=1 and h=96 0+2=2. Checking all pairs of g, h from 1, 96 through 47, 49 with GCD[g, h]=1, we find that for 97=42+55=2*3*7+5*11 we get 3+2=5 prime factors from g and h. So a(97)=5.
MATHEMATICA
Table[ct = 0; Do[h = n - g; If[GCD[g, h]==1, c=Length[FactorInteger[g]]+Length[FactorInteger[h]]; If[g == 1, c--]; If[h == 1, c--]; If[c > ct, ct = c]], {g, 1, Floor[n/2]}]; ct, {n, 3, 89}]
CROSSREFS
Sequence in context: A339929 A176835 A353865 * A078704 A306468 A032358
KEYWORD
nonn
AUTHOR
Lei Zhou, Feb 06 2014
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 23 11:44 EDT 2024. Contains 373644 sequences. (Running on oeis4.)