login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Products of cubes of 2 or more distinct primes.
2

%I #17 Aug 02 2024 21:25:49

%S 216,1000,2744,3375,9261,10648,17576,27000,35937,39304,42875,54872,

%T 59319,74088,97336,132651,166375,185193,195112,238328,274625,287496,

%U 328509,343000,405224,456533,474552,551368,614125,636056,658503,753571,804357,830584,857375

%N Products of cubes of 2 or more distinct primes.

%H Andrew Howroyd, <a href="/A177493/b177493.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A120944(n)^3. - _R. J. Mathar_, Dec 06 2010

%e 216 = 2^3 * 3^3.

%e 9261 = 3^3 * 7^3.

%e 27000 = 2^3 * 3^3 * 5^3.

%p q:= n-> not isprime(n) and numtheory[issqrfree](n):

%p map(x-> x^3, select(q, [$4..120]))[]; # _Alois P. Heinz_, Aug 02 2024

%t 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

%t Reap[Do[{p, e}=Transpose[FactorInteger[n]]; If[Length[p]>1 && Union[e]=={3}, Sow[n]], {n, 343000}]][[2, 1]]

%o (PARI) [k^3 | k<-[1..100], k>1 && !isprime(k) && issquarefree(k)] \\ _Andrew Howroyd_, Jan 14 2020

%o (Python)

%o from math import isqrt

%o from sympy import primepi, mobius

%o def A177493(n):

%o def f(x): return n+1+primepi(x)+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))

%o m, k = n+1, f(n+1)

%o while m != k:

%o m, k = k, f(k)

%o return m**3 # _Chai Wah Wu_, Aug 02 2024

%Y Cf. A000469, A085986, A162142, A177492.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, May 10 2010

%E Definition corrected by _R. J. Mathar_, Dec 06 2010

%E Terms a(25) and beyond from _Andrew Howroyd_, Jan 14 2020