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A130207 Diagonalized matrix of A000010, Euler totient function phi.

%I A130207 #15 Jan 17 2025 16:30:16
%S A130207 1,0,1,0,0,2,0,0,0,2,0,0,0,0,4,0,0,0,0,0,2,0,0,0,0,0,0,6,0,0,0,0,0,0,
%T A130207 0,4,0,0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,10,0,0,
%U A130207 0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,6
%N A130207 Diagonalized matrix of A000010, Euler totient function phi.
%H A130207 Antti Karttunen, <a href="/A130207/b130207.txt">Table of n, a(n) for n = 1..22155; the first 210 rows of the triangle</a>
%F A130207 T(n,n) = A000010(n).
%F A130207 T(n,k) = 0, if k <> n.
%e A130207 First few rows of the triangle are:
%e A130207 1;
%e A130207 0, 1;
%e A130207 0, 0, 2;
%e A130207 0, 0, 0, 2;
%e A130207 0, 0, 0, 0, 4;
%e A130207 ...
%p A130207 A130207 := proc(n,k)
%p A130207     if k = n then
%p A130207         numtheory[phi](n);
%p A130207     else
%p A130207         0;
%p A130207     end if;
%p A130207 end proc:
%p A130207 seq(seq(A130207(n,k),k=1..n),n=1..15) ;
%o A130207 (PARI) for(n=1,9,for(k=2,n,print1("0, "));print1(eulerphi(n)", ")) \\ _Charles R Greathouse IV_, Feb 19 2013
%o A130207 (PARI) A130207(n) = if(ispolygonal(n,3), eulerphi((sqrtint(1+(n*8))-1)/2), 0); \\ _Antti Karttunen_, Jan 17 2025
%Y A130207 Cf. A000010, A130208, A130209.
%K A130207 nonn,tabl,easy
%O A130207 1,6
%A A130207 _Gary W. Adamson_, May 16 2007
%E A130207 Data section extended up to a(105) by _Antti Karttunen_, Jan 17 2025