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A038109
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Divisible exactly by the square of a prime.
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12
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4, 9, 12, 18, 20, 25, 28, 36, 44, 45, 49, 50, 52, 60, 63, 68, 72, 75, 76, 84, 90, 92, 98, 99, 100, 108, 116, 117, 121, 124, 126, 132, 140, 144, 147, 148, 150, 153, 156, 164, 169, 171, 172, 175, 180, 188, 196, 198, 200, 204, 207, 212, 220, 225, 228, 234, 236, 242
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OFFSET
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1,1
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COMMENTS
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Numbers for which at least one prime factor exponent is exactly 2.
Sometimes called squarefull numbers, although that term is usually reserved for A001694. - N. J. A. Sloane, Jul 22 2012
The asymptotic density of this sequence is 1 - A330596 = 0.2514647... - Amiram Eldar, Aug 12 2020
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LINKS
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R. J. Mathar, Table of n, a(n) for n = 1..1247
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EXAMPLE
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20=5*2*2 is divisible by 2^2.
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MAPLE
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isA038109 := proc(n)
local p;
for p in ifactors(n)[2] do
if op(2, p) = 2 then
return true;
end if;
end do:
false ;
end proc: # R. J. Mathar, Dec 08 2015
# second Maple program:
q:= n-> ormap(i-> i[2]=2, ifactors(n)[2]):
select(q, [$1..300])[]; # Alois P. Heinz, Aug 12 2020
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MATHEMATICA
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Select[Range[250], MemberQ[Transpose[FactorInteger[#]][[2]], 2]&] (* Harvey P. Dale, Sep 24 2012 *)
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PROG
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(PARI) is(n)=#select(n->n==2, Set(factor(n)[, 2])) \\ Charles R Greathouse IV, Sep 17 2015
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CROSSREFS
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Cf. A001694, A013929, A284017, A284018.
Sequence in context: A081619 A336594 A304365 * A067259 A060687 A286228
Adjacent sequences: A038106 A038107 A038108 * A038110 A038111 A038112
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KEYWORD
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nonn,easy
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AUTHOR
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Felice Russo
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EXTENSIONS
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Corrected and extended by Erich Friedman
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STATUS
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approved
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