login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

a(n) = 1 if the product of exponents in the prime factorization of n is less than 3, otherwise 0.
5

%I #20 Jan 05 2023 03:20:11

%S 1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,0,1,1,

%T 1,0,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,0,1,0,1,1,1,1,1,1,1,0,1,1,1,1,

%U 1,1,1,0,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,1,1,1,1,0,1

%N a(n) = 1 if the product of exponents in the prime factorization of n is less than 3, otherwise 0.

%C a(n) = 1 if there are more unitary divisors of n (A034444) than non-unitary divisors of n (A048105), otherwise 0.

%H Antti Karttunen, <a href="/A359471/b359471.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>.

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.

%F a(n) = [A005361(n) < 3], where [ ] is the Iverson bracket.

%F a(n) = [A046660(n) < 2].

%F a(n) = [A048106(n) > 0].

%F a(n) = [A359431(n) == 0] = [A325973(n) == A326043(n)].

%F a(n) = A008966(n) + A359474(n).

%F a(n) >= A359475(n).

%F Sum_{k=1..n} a(k) ~ c * n, where c = A059956 + A271971 = 0.8086828238... . - _Amiram Eldar_, Jan 05 2023

%t a[n_] := If[2^(1 + PrimeNu[n]) > DivisorSigma[0, n], 1, 0]; Array[a, 100] (* _Amiram Eldar_, Jan 05 2023 *)

%o (PARI) A359471(n) = { (1==n) || (factorback(factor(n)[, 2])<3); }; \\ After function "is" given in A048107.

%Y Characteristic function of A048107.

%Y Cf. A005361, A008966, A034444, A048105, A048106, A325973, A326043, A359431, A359472, A359474, A359475.

%Y Cf. A059956, A271971.

%K nonn

%O 1

%A _Antti Karttunen_, Jan 04 2023