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%I #15 Dec 07 2019 00:47:43
%S 0,0,0,0,1,0,0,0,0,0,0,1,2,1,0,0,0,2,2,0,0,0,1,2,3,2,1,0,0,0,2,2,2,2,
%T 0,0,0,1,0,3,4,3,0,1,0,0,0,0,0,4,4,0,0,0,0,0,1,2,1,0,5,0,1,2,1,0,0,0,
%U 2,2,0,0,0,0,2,2,0,0,0,1,2,3,2,1,6,1,2,3,2,1,0,0,0,2,2,2,2,6,6,2,2,2,2,0,0,0,1,0,3,4,3,6,7,6,3,4,3,0,1,0
%N Square array read by antidiagonals: A(x,y) is the result from writing x and y in primorial base (A049345) and starting from their least significant ends, always choosing a minimal digit from each digit position, and converting back to decimal.
%H Antti Karttunen, <a href="/A324351/b324351.txt">Table of n, a(n) for n = 0..65702 (the first 362 antidiagonals of the array)</a>
%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A(x,y) = A276085(A324350(x,y)) = A276085(gcd(A276086(x), A276086(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: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 1: 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, ...
%e 2: 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, ...
%e 3: 0, 1, 2, 3, 2, 3, 0, 1, 2, 3, 2, 3, 0, ...
%e 4: 0, 0, 2, 2, 4, 4, 0, 0, 2, 2, 4, 4, 0, ...
%e 5: 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, ...
%e 6: 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, ...
%e 7: 0, 1, 0, 1, 0, 1, 6, 7, 6, 7, 6, 7, 6, ...
%e 8: 0, 0, 2, 2, 2, 2, 6, 6, 8, 8, 8, 8, 6, ...
%e 9: 0, 1, 2, 3, 2, 3, 6, 7, 8, 9, 8, 9, 6, ...
%e 10: 0, 0, 2, 2, 4, 4, 6, 6, 8, 8, 10, 10, 6, ...
%e 11: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 6, ...
%e 12: 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 12, ...
%e etc.
%e In primorial base, 5 is written as "21" (as 5 = 2*2 + 1*1) and 10 is written as "120" (as 10 = 1*6 + 2*2 + 0*1). Aligning them digit by digit (from the least significant end), and then always choosing a lesser digit leaves us with digits "020", which is 4 written in primorial base as 2*2 + 0*1 = 4, thus A(5,10) = A(10,5) = 4.
%o (PARI)
%o up_to = 65703; \\ = binomial(362+1,2)
%o A002110(n) = prod(i=1,n,prime(i));
%o A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
%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 A324351sq(row,col) = A276085(gcd(A276086(row),A276086(col)));
%o A324351list(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] = A324351sq(a-col,col))); (v); };
%o v324351 = A324351list(up_to);
%o A324351(n) = v324351[1+n]; \\ _Antti Karttunen_, Feb 25 2019
%Y Cf. A001477 (central diagonal), A002110, A049345, A276085, A276086, A324350.
%K nonn,base,tabl
%O 0,13
%A _Antti Karttunen_, Feb 25 2019
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