A177493 Products of cubes of 2 or more distinct primes.

216, 1000, 2744, 3375, 9261, 10648, 17576, 27000, 35937, 39304, 42875, 54872, 59319, 74088, 97336, 132651, 166375, 185193, 195112, 238328, 274625, 287496, 328509, 343000, 405224, 456533, 474552, 551368, 614125, 636056, 658503, 753571, 804357, 830584, 857375

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Formula

a(n) = A120944(n)^3. - R. J. Mathar, Dec 06 2010

Example

216 = 2^3 * 3^3.
9261 = 3^3 * 7^3.
27000 = 2^3 * 3^3 * 5^3.

Maple

q:= n-> not isprime(n) and numtheory[issqrfree](n):
map(x-> x^3, 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]=={3}, AppendTo[lst, n]], {n, 0, 9!}]; lst
Reap[Do[{p, e}=Transpose[FactorInteger[n]]; If[Length[p]>1 && Union[e]=={3}, Sow[n]], {n, 343000}]][[2, 1]]

Prog

(PARI) [k^3 | k<-[1..100], k>1 && !isprime(k) && issquarefree(k)] \\ Andrew Howroyd, Jan 14 2020
(Python)
from math import isqrt
from sympy import primepi, mobius
def A177493(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**3 # Chai Wah Wu, Aug 02 2024

Crossrefs

Cf. A000469, A085986, A162142, A177492.

Sequence in context: A109399 A111029 A124581 * A162142 A233859 A233853

Adjacent sequences: A177490 A177491 A177492 * A177494 A177495 A177496

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 10 2010

Extensions

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

Terms a(25) and beyond from Andrew Howroyd, Jan 14 2020

Status

approved