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URL: https://oeis.org/A177492

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A177492
Products of squares of 2 or more distinct primes.
17
36, 100, 196, 225, 441, 484, 676, 900, 1089, 1156, 1225, 1444, 1521, 1764, 2116, 2601, 3025, 3249, 3364, 3844, 4225, 4356, 4761, 4900, 5476, 5929, 6084, 6724, 7225, 7396, 7569, 8281, 8649, 8836, 9025, 10404, 11025, 11236, 12100, 12321, 12996, 13225, 13924
OFFSET
1,1
LINKS
Chai Wah Wu, Algorithms for Complementary Sequences, Integers (2025) Vol. 25, Art. No. A95. See p. 21.
FORMULA
a(n) = A120944(n)^2. - R. J. Mathar, Dec 06 2010
Sum_{n>=1} 1/a(n) = 15/Pi^2 - Sum_{p prime} 1/p^2 - 1 = A082020 - A085548 - 1 = 0.067570334594001073151... . - Amiram Eldar, Nov 23 2025
EXAMPLE
36 = 2^2*3^2, 100 = 2^2*5*2, 196 = 2^2*7^2, ..., 900 = 2^2*3^2*5^2, ...
MAPLE
q:= n-> not isprime(n) and numtheory[issqrfree](n):
map(x-> x^2, select(q, [$4..120]))[]; # Alois P. Heinz, Aug 02 2024
MATHEMATICA
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
Reap[Do[{p, e} = Transpose[FactorInteger[n]]; If[Length[p]>1 && Union[e]=={2}, Sow[n]], {n, 13225}]][[2, 1]]
(* Alternative: *)
Select[Range[120], And[CompositeQ[#], SquareFreeQ[#]] &]^2 (* Michael De Vlieger, Aug 17 2023 *)
PROG
(Python)
from math import isqrt
from sympy import primepi, mobius
def A177492(n):
def f(x): return n+1+primepi(x)+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
m, k = n+1, f(n+1)
while m != k:
m, k = k, f(k)
return m**2 # Chai Wah Wu, Aug 02 2024
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition corrected by R. J. Mathar, Dec 06 2010
STATUS
approved