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A295884 Number of exponents larger than 3 in the prime factorization of n.

%I A295884 #19 Nov 01 2020 21:42:40
%S A295884 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
%T A295884 0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
%U A295884 0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0
%N A295884 Number of exponents larger than 3 in the prime factorization of n.
%C A295884 a(1296) is the first term greater than 1, and a(810000) is the first term greater than 2. - _Harvey P. Dale_, Dec 22 2017
%H A295884 Antti Karttunen, <a href="/A295884/b295884.txt">Table of n, a(n) for n = 1..65537</a>
%H A295884 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A295884 Additive with a(p^e) = 1 when e > 3, 0 otherwise.
%F A295884 a(n) = A295659(n) - A295883(n).
%F A295884 a(n) = A056170(A062378(n)) = A056170(A003557(A003557(n))) = A001221(A003557^3(n)).
%F A295884 a(n) = A001221(A053164(n)) = A001221(A008835(n)).
%F A295884 Asymptotic mean: lim_{n->oo} (1/n) * Sum_{k=1..n} a(k) = Sum_{p prime} 1/p^4 = 0.076993... (A085964). - _Amiram Eldar_, Nov 01 2020
%e A295884 For n = 16 = 2^4, there is one exponent and it is larger than 3, thus a(16) = 1.
%e A295884 For n = 96 = 2^5 * 3^1, there are two exponents, and the other one is larger than 3, thus a(96) = 1.
%e A295884 For n = 1296 = 2^4 * 3^4, there are two exponents larger than 3, thus a(1296) = 2.
%t A295884 Array[Total@ Map[Boole[# > 3] &, FactorInteger[#][[All, -1]]] &, 120] (* _Michael De Vlieger_, Nov 29 2017 *)
%t A295884 Table[Count[FactorInteger[n][[All,2]],_?(#>3&)],{n,130}] (* _Harvey P. Dale_, Dec 22 2017 *)
%o A295884 (Scheme, with memoization-macro definec)
%o A295884 (definec (A295884 n) (if (= 1 n) 0 (+ (if (> (A067029 n) 3) 1 0) (A295884 (A028234 n)))))
%Y A295884 Cf. A000188, A001221, A003557, A008835, A053164, A056170, A062378, A085964, A295659, A295883.
%K A295884 nonn
%O A295884 1,1296
%A A295884 _Antti Karttunen_, Nov 29 2017