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A177492 Products of squares of 2 or more distinct primes.

%I A177492 #21 Aug 02 2024 21:24:25
%S A177492 36,100,196,225,441,484,676,900,1089,1156,1225,1444,1521,1764,2116,
%T A177492 2601,3025,3249,3364,3844,4225,4356,4761,4900,5476,5929,6084,6724,
%U A177492 7225,7396,7569,8281,8649,8836,9025,10404,11025,11236,12100,12321,12996,13225,13924
%N A177492 Products of squares of 2 or more distinct primes.
%H A177492 Michael De Vlieger, <a href="/A177492/b177492.txt">Table of n, a(n) for n = 1..10000</a>
%F A177492 a(n) = A120944(n)^2. - _R. J. Mathar_, Dec 06 2010
%e A177492 36=2^2*3^2, 100=2^2*5*2, 196=2^2*7^2,..900=2^2*3^2*5^2,..
%p A177492 q:= n-> not isprime(n) and numtheory[issqrfree](n):
%p A177492 map(x-> x^2, select(q, [$4..120]))[];  # _Alois P. Heinz_, Aug 02 2024
%t A177492 f1[n_]:=Length[Last/@FactorInteger[n]]; f2[n_]:=Union[Last/@FactorInteger[n]]; lst={};Do[If[f1[n]>1&&f2[n]=={2},AppendTo[lst,n]],{n,0,8!}];lst
%t A177492 Reap[Do[{p, e} = Transpose[FactorInteger[n]]; If[Length[p]>1 && Union[e]=={2}, Sow[n]], {n, 13225}]][[2, 1]]
%t A177492 (* Second program *)
%t A177492 Select[Range[120], And[CompositeQ[#], SquareFreeQ[#]] &]^2 (* _Michael De Vlieger_, Aug 17 2023 *)
%o A177492 (Python)
%o A177492 from math import isqrt
%o A177492 from sympy import primepi, mobius
%o A177492 def A177492(n):
%o A177492     def f(x): return n+1+primepi(x)+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
%o A177492     m, k = n+1, f(n+1)
%o A177492     while m != k:
%o A177492         m, k = k, f(k)
%o A177492     return m**2 # _Chai Wah Wu_, Aug 02 2024
%Y A177492 Cf. A000469, A074985, A085986, A120944, A162142.
%K A177492 nonn
%O A177492 1,1
%A A177492 _Vladimir Joseph Stephan Orlovsky_, May 10 2010
%E A177492 Definition corrected by _R. J. Mathar_, Dec 06 2010