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A359471
a(n) = 1 if the product of exponents in the prime factorization of n is less than 3, otherwise 0.
5
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, 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, 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
OFFSET
1
COMMENTS
a(n) = 1 if there are more unitary divisors of n (A034444) than non-unitary divisors of n (A048105), otherwise 0.
FORMULA
a(n) = [A005361(n) < 3], where [ ] is the Iverson bracket.
a(n) = [A046660(n) < 2].
a(n) = [A048106(n) > 0].
a(n) = [A359431(n) == 0] = [A325973(n) == A326043(n)].
a(n) = A008966(n) + A359474(n).
a(n) >= A359475(n).
Sum_{k=1..n} a(k) ~ c * n, where c = A059956 + A271971 = 0.8086828238... . - Amiram Eldar, Jan 05 2023
MATHEMATICA
a[n_] := If[2^(1 + PrimeNu[n]) > DivisorSigma[0, n], 1, 0]; Array[a, 100] (* Amiram Eldar, Jan 05 2023 *)
PROG
(PARI) A359471(n) = { (1==n) || (factorback(factor(n)[, 2])<3); }; \\ After function "is" given in A048107.
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 04 2023
STATUS
approved