A355937 a(n) = 1 if the number of divisors of n is a noncomposite, otherwise 0.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Index entries for sequences computed from exponents in factorization of n

Formula

a(n) = A080339(A000005(n)).

For all n >= 1, a(n) <= A010055(n).

Sum_{k=1..n} a(k) ~ n/log n. - Bill McEachen and Charles R Greathouse IV, Sep 11 2022

Mathematica

a[n_] := If[!CompositeQ[DivisorSigma[0, n]], 1, 0]; Array[a, 100] (* Amiram Eldar, Jul 21 2022 *)

Prog

(PARI) A355937(n) = ((1==n)||isprime(isprimepower(n)+1));

Crossrefs

Characteristic function of {1} UNION A009087.

Cf. A000005, A010055, A080339.

Cf. A355938.

Sequence in context: A071032 A071034 A089497 * A345950 A122895 A333248

Adjacent sequences: A355934 A355935 A355936 * A355938 A355939 A355940

Keyword

nonn

Author

Antti Karttunen, Jul 21 2022

Status

approved