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


%S 4,8,12,16,20,24,25,27,28,32,36,40,44,48,49,50,52,54,56,60,64,68,72,

%T 75,76,80,81,84,88,92,96,98,100,104,108,112,116,120,121,124,125,128,

%U 132,135,136,140,144,147,148,150,152,156,160,162,164,168,169,172,175,176

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

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

%C All positive multiples of 4 are in the sequence.

%C Or numbers n such that there is a smaller positive number j == n (mod 3) such that sqrt(j*n) is 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).

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

%F 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.

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

%Y Cf. A046790, A046791, A007913.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Jun 11 2016

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Last modified August 4 16:34 EDT 2020. Contains 336202 sequences. (Running on oeis4.)