A263251 - OEIS

%I #13 Nov 09 2015 16:06:41

%S 2,1,0,0,2,1,1,1,1,1,2,1,1,0,1,2,1,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,0,

%T 1,2,0,1,1,1,1,1,0,1,0,2,1,0,1,1,1,0,3,1,1,1,1,1,1,1,1,3,0,0,1,2,2,0,

%U 2,1,0,1,1,1,2,1,1,0,1,1,0,1,1,1,1,3,2,1,0,1,1,1,1,3,1,1,1,1,1,0,1,1,0,0,2,0,0,0,0,1,2,2,2,2,0,0,1,0,1,1,1

%N Odd bisection of A263087; number of solutions to x - d(x) = (2n+1)^2, where d(x) is the number of divisors of x (A000005).

%H Antti Karttunen, <a href="/A263251/b263251.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A263087(2*n + 1).

%o (PARI)

%o A060990(n) = { my(k = n + 2400, s=0); while(k > n, if(((k-numdiv(k)) == n),s++); k--;); s}; \\ Hard limit A002183(77)=2400 good for at least up to A002182(77) = 10475665200.

%o A263087(n) = A060990(n^2);

%o A263251(n) = A263087((2*n)+1);

%o p = 0; for(n=0, 10000, k = A263251(n); p += k; write("b263251.txt", n, " ", k); write("b263253.txt", n, " ", p)); \\ Compute A263251 and A263253 at the same time.

%o (Scheme) (define (A263251 n) (A263087 (+ n n 1)))

%Y Cf. A000005, A060990, A263087, A263250.

%Y Cf. also A263253 (partial sums).

%K nonn

%O 0,1

%A _Antti Karttunen_, Nov 07 2015