A177492 Products of squares of 2 or more distinct primes.

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

Author

Vladimir Joseph Stephan Orlovsky, May 10 2010

Keywords

• nonn

Examples

			36=2^2*3^2, 100=2^2*5*2, 196=2^2*7^2,..900=2^2*3^2*5^2,..
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000469, A074985, A085986, A120944, A162142.

Programs

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]]
(* Second program *)
Select[Range[120], And[CompositeQ[#], SquareFreeQ[#]] &]^2 (* Michael De Vlieger, Aug 17 2023 *)

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

Formula

a(n) = A120944(n)^2. - R. J. Mathar, Dec 06 2010

Extensions

Definition corrected by R. J. Mathar, Dec 06 2010