A263087 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).

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, 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, 1, 1, 1, 2, 3, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0

Offset: 0

Author

Antti Karttunen, Oct 12 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10082

Crossrefs

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

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

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

Cf. also A261088, A263088.

Programs

PARI

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.
A263087(n) = A060990(n^2);
for(n=0, 10082, write("b263087.txt", n, " ", A263087(n)));

Scheme

(define (A263087 n) (A060990 (A000290 n)))

Formula

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