A046386 Products of exactly four distinct primes.
210, 330, 390, 462, 510, 546, 570, 690, 714, 770, 798, 858, 870, 910, 930, 966, 1110, 1122, 1155, 1190, 1218, 1230, 1254, 1290, 1302, 1326, 1330, 1365, 1410, 1430, 1482, 1518, 1554, 1590, 1610, 1722, 1770, 1785, 1794, 1806, 1830, 1870, 1914, 1938, 1974
Offset: 1
Examples
210 = 2*3*5*7; 330 = 2*3*5*11; 390 = 2*3*5*13; 462 = 2*3*7*11.
Links
- T. D. Noe, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Mathematica
fQ[n_] := Last /@ FactorInteger[n] == {1, 1, 1, 1}; Select[ Range[2000], fQ[ # ] &] (* Robert G. Wilson v, Aug 04 2005 *) Select[Range[2000],PrimeNu[#]==PrimeOmega[#]==4&] (* Harvey P. Dale, Jan 05 2025 *) -
PARI
is(n)=factor(n)[,2]==[1,1,1,1]~ \\ Charles R Greathouse IV, Sep 17 2015
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PARI
is(n) = omega(n)==4 && bigomega(n)==4 \\ Hugo Pfoertner, Dec 18 2018
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PARI
list(lim)=my(v=List()); forprime(p=2,sqrtnint(lim\=1,4), forprime(q=p+1,sqrtnint(lim\p,3), forprime(r=q+2,sqrtint(lim\p\q), my(t=p*q*r); forprime(s=r+2,lim\t, listput(v,t*s))))); Set(v) \\ Charles R Greathouse IV, Dec 05 2024
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Python
from math import isqrt from sympy import primepi, primerange, integer_nthroot def A046386(n): def f(x): return int(n+x-sum(primepi(x//(k*m*r))-c for a,k in enumerate(primerange(integer_nthroot(x,4)[0]+1),1) for b,m in enumerate(primerange(k+1,integer_nthroot(x//k,3)[0]+1),a+1) for c,r in enumerate(primerange(m+1,isqrt(x//(k*m))+1),b+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 bisection(f) # Chai Wah Wu, Aug 29 2024
Formula
Intersection of A014613 (product of 4 primes) and A033993 (divisible by 4 distinct primes). - M. F. Hasler, Mar 24 2022
Comments