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

1,8

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).

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.

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.

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A083910 A069843 A069849 * A072507 A004530 A368980

Adjacent sequences: A138042 A138043 A138044 * A138046 A138047 A138048

Keyword

nonn,tabl

Author

Mats Granvik, Mar 02 2008

Status

approved