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A096917
Smallest prime factor of n-th product of 3 distinct primes.
8
2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 5, 3, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 5, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 5, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 5, 2, 2, 2, 3, 2, 5, 2, 3, 2, 2, 3, 2, 3, 2
OFFSET
1,1
a(n)*A096918(n)*A096919(n) = A007304(n); a(n) < A096918(n) < A096919(n);
a(n) = A020639(A007304(n)).
MATHEMATICA
f[n_]:=Last/@FactorInteger[n]=={1, 1, 1}; f1[n_]:=Min[First/@FactorInteger[n]]; f2[n_]:=Max[First/@FactorInteger[n]]; lst={}; Do[If[f[n], AppendTo[lst, f1[n]]], {n, 0, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 10 2010 *)
PROG
(Python)
from math import isqrt
from sympy import primepi, primerange, integer_nthroot, primefactors
def A096917(n):
def f(x): return int(n+x-sum(primepi(x//(k*m))-b for a, k in enumerate(primerange(integer_nthroot(x, 3)[0]+1), 1) for b, m in enumerate(primerange(k+1, isqrt(x//k)+1), a+1)))
def bisection(f, kmin=0, kmax=1):
while f(kmax) > kmax: kmax <<= 1
while kmax-kmin > 1:
kmid = kmax+kmin>>1
if f(kmid) <= kmid:
kmax = kmid
else:
kmin = kmid
return kmax
return min(primefactors(bisection(f))) # Chai Wah Wu, Aug 30 2024
CROSSREFS
Sequence in context: A258757 A351399 A024708 * A336664 A335108 A359238
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jul 15 2004
STATUS
approved

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Last modified September 20 06:55 EDT 2024. Contains 376067 sequences. (Running on oeis4.)