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

1,1

Links

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

Formula

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

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]]
(* Second program *)
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

Crossrefs

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

Sequence in context: A303661 A175391 A030627 * A077448 A085986 A027603

Adjacent sequences: A177489 A177490 A177491 * A177493 A177494 A177495

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 10 2010

Extensions

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

Status

approved