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A334230
Triangle read by rows: T(n,k) gives the meet of n and k in the graded lattice of the positive integers defined by covering relations "n covers (n - n/p)" for all divisors p of n.
4
1, 1, 2, 1, 2, 3, 1, 2, 2, 4, 1, 2, 2, 4, 5, 1, 2, 3, 4, 4, 6, 1, 2, 3, 4, 4, 6, 7, 1, 2, 2, 4, 4, 4, 4, 8, 1, 2, 3, 4, 4, 6, 6, 4, 9, 1, 2, 2, 4, 5, 4, 4, 8, 4, 10, 1, 2, 2, 4, 5, 4, 4, 8, 4, 10, 11, 1, 2, 3, 4, 4, 6, 6, 8, 6, 8, 8, 12, 1, 2, 3, 4, 4, 6, 6, 8
OFFSET
1,3
COMMENTS
Any row with prime index p is a copy of row p-1 followed by that prime p.
FORMULA
T(n, k) = m*T(n/m, k/m) for m = gcd(n, k).
EXAMPLE
The interval [1,15] illustrates that, for example, T(12, 10) = 8, T(12, 4) = T(5, 6) = 4, T(8, 3) = 2, etc.
15
_/ \_
/ \
10 12
| \_ _/ |
| \ / |
5 8 6
\_ | _/|
\_|_/ |
4 3
| _/
|_/
2
|
|
1
Triangle begins:
n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14
---+---------------------------------
1 | 1
2 | 1 2
3 | 1 2 3
4 | 1 2 2 4
5 | 1 2 2 4 5
6 | 1 2 3 4 4 6
7 | 1 2 3 4 4 6 7
8 | 1 2 2 4 4 4 4 8
9 | 1 2 3 4 4 6 6 4 9
10 | 1 2 2 4 5 4 4 8 4 10
11 | 1 2 2 4 5 4 4 8 4 10 11
12 | 1 2 3 4 4 6 6 8 6 8 8 12
13 | 1 2 3 4 4 6 6 8 6 8 8 12 13
14 | 1 2 3 4 4 6 7 8 6 8 8 12 12 14
PROG
(PARI)
\\ This just returns the largest (in a normal sense) number x from the intersection of the set of descendants of n and k:
up_to = 105;
buildWdescsets(up_to) = { my(v=vector(up_to)); v[1] = Set([1]); for(n=2, up_to, my(f=factor(n)[, 1]~, s=Set([n])); for(i=1, #f, s = setunion(s, v[n-(n/f[i])])); v[n] = s); (v); }
vdescsets = buildWdescsets(up_to);
A334230tr(n, k) = vecmax(setintersect(vdescsets[n], vdescsets[k]));
A334230list(up_to) = { my(v = vector(up_to), i=0); for(n=1, oo, for(k=1, n, i++; if(i > up_to, return(v)); v[i] = A334230tr(n, k))); (v); };
v334230 = A334230list(up_to);
A334230(n) = v334230[n]; \\ Antti Karttunen, Apr 19 2020
CROSSREFS
KEYWORD
nonn,tabl,look
AUTHOR
STATUS
approved