A353798 a(n) = 1 if n is either 4th power of a prime (A030514), or product of a prime and the square of a different prime (A054753), otherwise 0.

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

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) = [floor(A101296(n)/2) == 3], where [ ] is the Iverson bracket, giving in this case 1 only if the prime signature class of n (A101296) is either 6 or 7.

a(n) >= A353472(n).

Mathematica

a[n_] := If[MemberQ[{{4}, {1, 2}, {2, 1}}, FactorInteger[n][[;; , 2]]], 1, 0]; Array[a, 100] (* Amiram Eldar, May 13 2022 *)

Prog

(PARI) A353798(n) = { my(f=factor(n)[, 2]~); (f==[4] || f==[2, 1] || f==[1, 2]); }; \\ From function "is" in A080258

Crossrefs

Characteristic function of A080258.

Cf. A030514, A054753, A101296, A353472.

Sequence in context: A355447 A045701 A277156 * A193095 A011725 A346619

Adjacent sequences: A353795 A353796 A353797 * A353799 A353800 A353801

Keyword

nonn

Author

Antti Karttunen, May 13 2022

Status

approved