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%I #9 Mar 05 2023 13:26:43
%S 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,
%T 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,
%U 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
%N Triangle read by rows: largest proper divisor of n as a table, ones excluded.
%C 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).
%H Antti Karttunen, <a href="/A138045/b138045.txt">Table of n, a(n) for n = 1..23220</a> (the first 215 rows of the triangle).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ProperDivisor.html">Proper Divisor</a>.
%F 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.
%e The first few terms of the table are:
%e 0
%e 0,0
%e 0,0,0
%e 0,2,0,0
%e 0,0,0,0,0
%e 0,0,3,0,0,0
%e 0,0,0,0,0,0,0
%e 0,0,0,4,0,0,0,0
%e 0,0,3,0,0,0,0,0,0
%o (PARI)
%o up_to = 23220; \\ binomial(215+1,2)
%o A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
%o A138045tr(n, k) = if((k>1) && (A032742(n)==k), k, 0);
%o 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); };
%o v138045 = A138045list(up_to);
%o A138045(n) = v138045[n]; \\ _Antti Karttunen_, Dec 24 2018
%Y Cf. A001248, A016945, A084967, A007310, A127093, A032742, A007775.
%K nonn,tabl
%O 1,8
%A _Mats Granvik_, Mar 02 2008
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