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A274141 Positive numbers divisible by 3^3 or by the square of some other prime. 3
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 (list; graph; refs; listen; history; text; internal format)
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 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

Table of n, a(n) for n=1..60.

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.

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: A190714 A311123 A285466 * A086133 A100716 A328251

Adjacent sequences:  A274138 A274139 A274140 * A274142 A274143 A274144

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Jun 11 2016

STATUS

approved

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Last modified July 4 16:24 EDT 2020. Contains 335448 sequences. (Running on oeis4.)