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a(n) = 1 if n is a cubefree nonsquare whose factorization into a product of primes contains exactly one square, otherwise 0.
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%I #14 Jan 05 2023 03:19:58

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

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

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

%N a(n) = 1 if n is a cubefree nonsquare whose factorization into a product of primes contains exactly one square, otherwise 0.

%H Antti Karttunen, <a href="/A359475/b359475.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) = A049240(n) * A359474(n) = A359474(n) - A302048(n).

%F a(n) <= A359471(n).

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

%t a[n_] := If[PrimeNu[n] > 1 && PrimeOmega[n] - PrimeNu[n] == 1, 1, 0]; Array[a, 100] (* _Amiram Eldar_, Jan 05 2023 *)

%o (PARI) A359475(n) = (omega(n) > 1) && (bigomega(n) - omega(n) == 1); \\ From "isok" function given in A072357 by _Michel Marcus_, Jul 16 2015

%Y Characteristic function of A072357.

%Y Cf. A049240, A271971, A302048, A359471, A359474.

%K nonn

%O 1

%A _Antti Karttunen_, Jan 04 2023