A324823 a(n) = 1 if n > 1 and A156552(n) is a square or a twice a square, 0 otherwise.

0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to binary expansion of n

Index entries for characteristic functions

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = A323243(n) mod 2.

For n > 1, a(n) = A053866(A156552(n)).

Prog

(PARI)
A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552 by David A. Corneth
A324823(n) = if(1==n, 0, n=A156552(n); (issquare(n) || (!(n%2) && issquare(n/2))));

Crossrefs

Characteristic function (for n > 1) of A324813.

Cf. A053866, A156552, A323243, A324822, A324824, A324825 (inverse Möbius transform).

Sequence in context: A204175 A343173 A285255 * A353354 A284912 A192082

Adjacent sequences: A324820 A324821 A324822 * A324824 A324825 A324826

Keyword

nonn

Author

Antti Karttunen, Mar 16 2019

Status

approved