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

1,1

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

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A046790, A046791, A007913.

Sequence in context: A311123 A367086 A285466 * A086133 A100716 A328251

Adjacent sequences: A274138 A274139 A274140 * A274142 A274143 A274144

Keyword

nonn

Author

Vladimir Shevelev, Jun 11 2016

Status

approved