A237354 -id:A237354 - cp's OEIS frontend

A237359 a(n) is the largest integer that makes A237354(a(n))=n.

2, 3, 7, 23, 89, 389, 2297, 13903, 82829, 508847

Offset: 0

Lei Zhou, Feb 06 2014

a(0)-a(7) are primes, while a(8) = 113*733. Probably, a(9) = 508847 and a(10) = 3699977. - Giovanni Resta, Feb 23 2014

Probably, a(11) = 28644529 and a(12) = 235037603. - Hiroaki Yamanouchi, Oct 02 2014

			A237354(2)=0 and this is the only 0 in A237354. So a(0)=2;
A237354(3)=1 and this is the only 1 in A237354. So a(1)=3;
A237354(4,5,6,7)=2, the largest one is A237354(7).  So a(2)=7;
There are 10 numbers between (include) 8 and 23 that make A237354(n)=3.  The largest one is 23.  There is no more A237354(n)=3 checked up to n=2*3*5+1=31.  So a(3)=23;
Checked up to n=2*3*5*7+1=211, we got a(4)=89;
Checked up to n=2*3*5*7*11+1=2311, we got a(5)=389;
Checked up to n=2*3*5*7*11*13+1=30031, we got a(6)=2297;

Cf. A237354.

a(8) from Giovanni Resta, Feb 23 2014

a(9) from Hiroaki Yamanouchi, Oct 02 2014

A237110 Maximum number of distinct prime factors of pairs of coprime g and h (g < h) adding to n.

Original entry on oeis.org

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

Offset: 3

Lei Zhou, Feb 06 2014

nonn

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)#.

			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.

Lei Zhou, Table of n, a(n) for n = 3..10000

Cf. A237354, A182987, A002110

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}]

cp's OEIS Frontend

A237359 a(n) is the largest integer that makes A237354(a(n))=n.

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