login
a(n) = A060990(n^2); number of solutions to x - d(x) = n^2, where d(x) is the number of divisors of x (A000005).
7

%I #14 Nov 08 2015 04:47:20

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

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

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

%N a(n) = A060990(n^2); number of solutions to x - d(x) = n^2, where d(x) is the number of divisors of x (A000005).

%H Antti Karttunen, <a href="/A263087/b263087.txt">Table of n, a(n) for n = 0..10082</a>

%F a(n) = A060990(n^2) = A060990(A000290(n)).

%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 for(n=0, 10082, write("b263087.txt", n, " ", A263087(n)));

%o (Scheme) (define (A263087 n) (A060990 (A000290 n)))

%Y Cf. A000005, A000290, A002182, A002183, A060990.

%Y Cf. A263093 (positions of zeros), A263092 (nonzeros).

%Y Cf. A263250, A263251 (bisections) and A263252, A263253 (their partial sums).

%Y Cf. also A261088, A263088.

%K nonn

%O 0,1

%A _Antti Karttunen_, Oct 12 2015