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%I #12 Feb 26 2019 08:19:06
%S 1,1,1,1,2,1,1,1,1,1,1,2,3,2,1,1,1,3,3,1,1,1,2,3,6,3,2,1,1,1,3,3,3,3,
%T 1,1,1,2,1,6,9,6,1,2,1,1,1,1,1,9,9,1,1,1,1,1,2,3,2,1,18,1,2,3,2,1,1,1,
%U 3,3,1,1,1,1,3,3,1,1,1,2,3,6,3,2,5,2,3,6,3,2,1,1,1,3,3,3,3,5,5,3,3,3,3,1,1,1,2,1,6,9,6,5,10,5,6,9,6,1,2,1
%N Square array read by antidiagonals: A(x,y) = gcd(A276086(x),A276086(y)), for x, y >= 0.
%H Antti Karttunen, <a href="/A324350/b324350.txt">Table of n, a(n) for n = 0..7259 (the first 120 antidiagonals of the array)</a>
%H Antti Karttunen, <a href="/A324350/a324350.txt">Data supplement: n, a(n) computed for n = 0..65702</a>
%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A(x,y) = gcd(A276086(x), A276086(y)).
%F A(x,y) = A276086(A324351(x,y)).
%e The array A begins:
%e 0 1 2 3 4 5 6 7 8 9 10 11 12
%e x/y ------------------------------------------------------
%e 0: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e 1: 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, ...
%e 2: 1, 1, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 1, ...
%e 3: 1, 2, 3, 6, 3, 6, 1, 2, 3, 6, 3, 6, 1, ...
%e 4: 1, 1, 3, 3, 9, 9, 1, 1, 3, 3, 9, 9, 1, ...
%e 5: 1, 2, 3, 6, 9, 18, 1, 2, 3, 6, 9, 18, 1, ...
%e 6: 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, ...
%e 7: 1, 2, 1, 2, 1, 2, 5, 10, 5, 10, 5, 10, 5, ...
%e 8: 1, 1, 3, 3, 3, 3, 5, 5, 15, 15, 15, 15, 5, ...
%e 9: 1, 2, 3, 6, 3, 6, 5, 10, 15, 30, 15, 30, 5, ...
%e 10: 1, 1, 3, 3, 9, 9, 5, 5, 15, 15, 45, 45, 5, ...
%e 11: 1, 2, 3, 6, 9, 18, 5, 10, 15, 30, 45, 90, 5, ...
%e 12: 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 25, ...
%o (PARI)
%o up_to = 65703; \\ = binomial(362+1,2)
%o A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
%o A324350sq(row,col) = gcd(A276086(row),A276086(col));
%o A324350list(up_to) = { my(v = vector(up_to), i=0); for(a=0,oo, for(col=0,a, if(i++ > up_to, return(v)); v[i] = A324350sq(a-col,col))); (v); };
%o v324350 = A324350list(up_to);
%o A324350(n) = v324350[1+n];
%Y Cf. A003989, A276086 (central diagonal), A324198, A324351.
%K nonn,tabl
%O 0,5
%A _Antti Karttunen_, Feb 25 2019
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