A138045 Triangle read by rows: largest proper divisor of n as a table, ones excluded.

0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Mats Granvik, Mar 02 2008

Keywords

• nonn
• tabl

Comments

The numbers in the triangle form lines that begin at T(A001248,A000040). The first line of numbers from the right, is T(A005843,A000027). The second line is T(A016945,A005408). The third line is T(A084967,A007310).

Examples

			The first few terms of the table are:
  0
  0,0
  0,0,0
  0,2,0,0
  0,0,0,0,0
  0,0,3,0,0,0
  0,0,0,0,0,0,0
  0,0,0,4,0,0,0,0
  0,0,3,0,0,0,0,0,0
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..23220 (the first 215 rows of the triangle).
• Eric Weisstein's World of Mathematics, Proper Divisor.

Crossrefs

Cf. A001248, A016945, A084967, A007310, A127093, A032742, A007775.

Programs

PARI

up_to = 23220; \\ binomial(215+1,2)
A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A138045tr(n, k) = if((k>1) && (A032742(n)==k), k, 0);
A138045list(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] = A138045tr(n,k))); (v); };
v138045 = A138045list(up_to);
A138045(n) = v138045[n]; \\ Antti Karttunen, Dec 24 2018

Formula

T(n,k) = if k==A032742(n) and n(T(n,k))==n(A032742(n)) and k>1 then k else 0 (1<=k<=n), T(1,1)=0.