cp's OEIS Frontend

A177493 Products of cubes of 2 or more distinct primes.

%I A177493 #17 Aug 02 2024 21:25:49
%S A177493 216,1000,2744,3375,9261,10648,17576,27000,35937,39304,42875,54872,
%T A177493 59319,74088,97336,132651,166375,185193,195112,238328,274625,287496,
%U A177493 328509,343000,405224,456533,474552,551368,614125,636056,658503,753571,804357,830584,857375
%N A177493 Products of cubes of 2 or more distinct primes.
%H A177493 Andrew Howroyd, <a href="/A177493/b177493.txt">Table of n, a(n) for n = 1..1000</a>
%F A177493 a(n) = A120944(n)^3. - _R. J. Mathar_, Dec 06 2010
%e A177493 216 = 2^3 * 3^3.
%e A177493 9261 = 3^3 * 7^3.
%e A177493 27000 = 2^3 * 3^3 * 5^3.
%p A177493 q:= n-> not isprime(n) and numtheory[issqrfree](n):
%p A177493 map(x-> x^3, select(q, [$4..120]))[];  # _Alois P. Heinz_, Aug 02 2024
%t A177493 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 A177493 Reap[Do[{p, e}=Transpose[FactorInteger[n]]; If[Length[p]>1 && Union[e]=={3}, Sow[n]], {n, 343000}]][[2, 1]]
%o A177493 (PARI) [k^3 | k<-[1..100], k>1 && !isprime(k) && issquarefree(k)] \\ _Andrew Howroyd_, Jan 14 2020
%o A177493 (Python)
%o A177493 from math import isqrt
%o A177493 from sympy import primepi, mobius
%o A177493 def A177493(n):
%o A177493     def f(x): return n+1+primepi(x)+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
%o A177493     m, k = n+1, f(n+1)
%o A177493     while m != k:
%o A177493         m, k = k, f(k)
%o A177493     return m**3 # _Chai Wah Wu_, Aug 02 2024
%Y A177493 Cf. A000469, A085986, A162142, A177492.
%K A177493 nonn
%O A177493 1,1
%A A177493 _Vladimir Joseph Stephan Orlovsky_, May 10 2010
%E A177493 Definition corrected by _R. J. Mathar_, Dec 06 2010
%E A177493 Terms a(25) and beyond from _Andrew Howroyd_, Jan 14 2020