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

0,1

Links

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

Formula

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

Prog

(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)))

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.

Sequence in context: A123550 A320638 A262045 * A204433 A004578 A319372

Adjacent sequences: A263084 A263085 A263086 * A263088 A263089 A263090

Keyword

nonn

Author

Antti Karttunen, Oct 12 2015

Status

approved