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

Author

Vladimir Joseph Stephan Orlovsky, May 10 2010

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A000469, A085986, A162142, A177492.

Programs

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]]

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

Formula

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

Extensions

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

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