A274141 Positive numbers divisible by 3^3 or by the square of some other prime.

4, 8, 12, 16, 20, 24, 25, 27, 28, 32, 36, 40, 44, 48, 49, 50, 52, 54, 56, 60, 64, 68, 72, 75, 76, 80, 81, 84, 88, 92, 96, 98, 100, 104, 108, 112, 116, 120, 121, 124, 125, 128, 132, 135, 136, 140, 144, 147, 148, 150, 152, 156, 160, 162, 164, 168, 169, 172, 175, 176

Offset: 1

Author

Vladimir Shevelev, Jun 11 2016

Keywords

• nonn

Comments

Or numbers n>=4 having a divisor k^2>=4 such that n and n/k^2 equal modulo 3.

All positive multiples of 4 are in the sequence.

Or numbers n such that there is a smaller positive number j == n (mod 3) such that sqrt(j*n) is an integer. The smallest such j corresponds to the greatest k; or, the same, j = 3*A007913(n/3), if n is divisible by 3 and otherwise j=A007913(n).

Or complement to the sequence: S, 3*S and 9*S, where S denotes the sequence of the squarefree numbers not divisible by 3.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A046790, A046791, A007913.

Programs

Mathematica

Select[Range[200], (e = IntegerExponent[#, 3]) > 2 || ! SquareFreeQ[#/3^e] &] (* Amiram Eldar, Feb 25 2021 *)

PARI

isok(n) = (((v=valuation(n, 3)) >= 3) || (((m = n/3^v) > 1) && (vecmax((factor(m))[,2]) >=2))); \\ Michel Marcus, Jun 12 2016

Formula

Let A(x) be the number of a(n)<=x. Then A(x)~(1 - 6.5/Pi^2)*x = 0.34141230...*x as x goes to infinity.