A374016 a(n) = 1 if n is a fourth power, else 0.

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

Offset

0

Links

Antti Karttunen, Table of n, a(n) for n = 0..100000

Peter Bala, A continuous interpolating function for A374016.

Index entries for characteristic functions.

Index entries for sequences computed from exponents in factorization of n.

Formula

G.f.: Sum_{k>=0} x^(k^4).

For n >= 1, a(n) = (1/4) * lim_{x -> n} sin(Pi*x)/(x^(3/4) * sin(Pi*x^(1/4))) = (3/4) * lim_{x -> n} sin(Pi*x)/(x^(1/4) * sin(Pi*x^(3/4))). Cf. A010057. - Peter Bala, Sep 07 2025

Multiplicative with a(p^e) = A121262(e). - Amiram Eldar, Oct 31 2025

Mathematica

Array[Boole[IntegerQ[#^(1/4)]] &, 100, 0] (* Paolo Xausa, Jul 02 2024 *)

Prog

(PARI) a(n) = ispower(n, 4);
(PARI) my(N=110, x='x+O('x^N)); Vec(sum(k=0, sqrtnint(N, 4), x^k^4))

Crossrefs

Characteristic function of A000583.

Cf. A005369, A010052, A010054, A010057, A121262, A132918, A199918.

Sequence in context: A016422 A016399 A016383 * A279485 A298859 A216280

Adjacent sequences: A374013 A374014 A374015 * A374017 A374018 A374019

Keyword

nonn,easy,mult

Author

Seiichi Manyama, Jun 25 2024

Status

approved