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%I #12 Jun 10 2020 22:45:50
%S 1,0,1,1,0,0,0,0,2,1,0,1,0,0,0,0,1,0,0,0,1,0,2,0,1,0,1,2,0,0,0,0,0,0,
%T 1,0,0,0,0,1,1,0,0,0,0,0,0,0,2,1,0,0,0,0,0,2,0,1,0,2,0,1,0,1,0,2,0,0,
%U 0,0,0,0,1,0,2,1,0,0,0,0,0,0,0,0,2,0,1
%N Number of partitions of n-th semiprime into 2 squares.
%C See also A000161 Number of partitions of n into 2 squares (when order does not matter and zero is allowed).
%C From _Robert Israel_, Jun 10 2020: (Start)
%C a(1)=1 if A001358(n) = p^2 where p is not in A002144.
%C a(n)=1 if A001358(n) = 2*p where p is in A002144.
%C a(n)=2 if A001358(n) = p*q where p and q are in A002144 (not necessarily distinct).
%C a(n)=0 otherwise. (End)
%H Robert Israel, <a href="/A116852/b116852.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A000161(A001358(n)).
%e a(1) = 1 because semiprime(1) = 4 = 0^2 + 2^2, the unique sum of squares.
%e a(2) = 0 because semiprime(2) = 6 has no decomposition into sum of 2 squares because it has a prime factor p == 3 (mod 4) with an odd power.
%e a(3) = 1 because semiprime(3) = 9 = 0^2 + 3^2, the unique sum of squares.
%e a(4) = 1 because semiprime(4) = 10 = 2*5 = 1^2 + 3^2.
%e a(9) = 2 because semiprime(9) = 25 = 0^2 + 5^2 = 3^2 + 4^2, two distinct ways.
%e a(23) = 2 because semiprime(23) = 65 = 5*13 = 1^2 + 8^2 = 4^2 + 7^2.
%e a(28) = 2 because semiprime(28) = 85 = 5*17 = 2^2 + 9^2 = 6^2 + 7^2.
%e a(49) = 2 because semiprime(49) = 145 = 5*29 = 1^2 + 12^2 = 8^2 + 9^2.
%e a(56) = 2 because semiprime(56) = 169 = 0^2 + 13^2 = 5^2 + 12^2.
%e a(60) = 2 because semiprime(60) = 185 = 5*37 = 4^2 + 13^2 = 8^2 + 11^2.
%p R:= NULL: count:= 0:
%p for n from 4 while count < 100 do
%p if numtheory:-bigomega(n) = 2 then
%p count:= count+1;
%p F:= ifactors(n)[2];
%p if nops(F) = 1 then
%p if F[1][1] mod 4 = 1 then v:= 2
%p else v:= 1
%p fi
%p elif F[1][1]=2 and F[2][1] mod 4 = 1 then v:= 1
%p elif F[1][1] mod 4 = 1 and F[2][1] mod 4 = 1 then v:= 2
%p else v:= 0
%p fi;
%p R:= R, v;
%p fi
%p od:
%p R; # _Robert Israel_, Jun 10 2020
%Y Cf. A000161, A001358.
%K easy,nonn
%O 1,9
%A _Jonathan Vos Post_, Mar 15 2006
%E More terms from _Giovanni Resta_, Jun 15 2016
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