A353625 - OEIS

%I #12 Jul 24 2022 03:55:44

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

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

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

%N a(n) = 1 if n is divisible by the squares of two distinct primes, otherwise 0.

%H Antti Karttunen, <a href="/A353625/b353625.txt">Table of n, a(n) for n = 1..65537</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) = 1 iff A056170(n) > 1, otherwise 0.

%F a(n) = a(A046523(n)).

%F a(n) <= A353626(n).

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 - (6/Pi^2) * (1 + A154945) = 0.05668359058... . - _Amiram Eldar_, Jul 24 2022

%t a[n_] := If[Count[FactorInteger[n][[;; , 2]], _?(# > 1 &)] > 1, 1, 0]; Array[a, 100] (* _Amiram Eldar_, Jul 24 2022 *)

%o (PARI)

%o A056170(n) = { my(f=factor(n)[, 2]); sum(i=1, #f, f[i]>1); }; \\ From A056170

%o A353625(n) = (A056170(n)>1);

%Y Characteristic function of A036785.

%Y Cf. A046523, A056170, A154945, A353626.

%K nonn

%O 1

%A _Antti Karttunen_, May 02 2022