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A036785 Numbers divisible by the squares of two distinct primes. 14

%I #34 Mar 05 2021 21:48:04

%S 36,72,100,108,144,180,196,200,216,225,252,288,300,324,360,392,396,

%T 400,432,441,450,468,484,500,504,540,576,588,600,612,648,675,676,684,

%U 700,720,756,784,792,800,828,864,882,900,936,968,972,980,1000,1008,1044

%N Numbers divisible by the squares of two distinct primes.

%C Not squarefree, not a nontrivial prime power and not in {squarefree} times {nontrivial prime powers}.

%C Numbers k such that A056170(k) > 1. The asymptotic density of this sequence is 1 - (6/Pi^2) * (1 + A154945) = 0.05668359058... - _Amiram Eldar_, Nov 01 2020

%D CRC Standard Mathematical Tables and Formulae, 30th ed., (1996) page 102-105.

%H Charles R Greathouse IV, <a href="/A036785/b036785.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Range@ 1050, And[Length@ # > 1, Total@ Boole@ Map[# > 1 &, #[[All, -1]]] > 1] &@ FactorInteger@ # &] (* _Michael De Vlieger_, Apr 25 2017 *)

%t dstdpQ[n_]:=Length[Select[Sqrt[#]&/@Divisors[n],PrimeQ]]>1; Select[ Range[ 1100],dstdpQ] (* _Harvey P. Dale_, Jan 15 2020 *)

%o (PARI) is(n)=my(f=vecsort(factor(n)[,2],,4));#f>1&&f[2]>1 \\ _Charles R Greathouse IV_, Nov 15 2012

%Y Cf. A005117, A025475, A056170, A154945.

%Y Equivalent sequence for 3 distinct primes: A318720.

%Y Cf. A085986, A338539, A339245 (subsequences).

%Y Subsequence of A038838.

%K easy,nonn

%O 1,1

%A _Alford Arnold_

%E More terms from Larry Reeves (larryr(AT)acm.org), Apr 03 2000

%E New name from _Charles R Greathouse IV_, Nov 15 2012

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Last modified April 24 20:08 EDT 2024. Contains 371963 sequences. (Running on oeis4.)