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

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, 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, 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

Offset: 1

Author

Antti Karttunen, Nov 29 2017

Keywords

• nonn

Comments

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

Examples

			For n = 16 = 2^4, there is one exponent and it is larger than 3, thus a(16) = 1.
For n = 96 = 2^5 * 3^1, there are two exponents, and the other one is larger than 3, thus a(96) = 1.
For n = 1296 = 2^4 * 3^4, there are two exponents larger than 3, thus a(1296) = 2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A000188, A001221, A003557, A008835, A053164, A056170, A062378, A085964, A295659, A295883.

Programs

Mathematica

Array[Total@ Map[Boole[# > 3] &, FactorInteger[#][[All, -1]]] &, 120] (* Michael De Vlieger, Nov 29 2017 *)
Table[Count[FactorInteger[n][[All,2]],?(#>3&)],{n,130}] (* _Harvey P. Dale, Dec 22 2017 *)

Formula

Additive with a(p^e) = 1 when e > 3, 0 otherwise.

a(n) = A295659(n) - A295883(n).

a(n) = A056170(A062378(n)) = A056170(A003557(A003557(n))) = A001221(A003557^3(n)).

a(n) = A001221(A053164(n)) = A001221(A008835(n)).

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