A179691 Numbers p^5*q^2*r where p, q, r are 3 distinct primes.
1440, 2016, 2400, 3168, 3744, 4704, 4860, 4896, 5472, 5600, 6624, 6804, 7840, 8352, 8800, 8928, 10400, 10656, 10692, 11616, 11808, 12150, 12384, 12636, 13536, 13600, 15200, 15264, 16224, 16524, 16992, 17248, 17568, 18400, 18468, 19296, 19360
Offset: 1
Keywords
Links
- T. D. Noe, Table of n, a(n) for n = 1..1000
- Will Nicholes, List of Prime Signatures
- Index to sequences related to prime signature
Crossrefs
Programs
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Mathematica
f[n_]:=Sort[Last/@FactorInteger[n]]=={1,2,5}; Select[Range[20000], f] -
PARI
list(lim)=my(v=List(),t1,t2);forprime(p=2, (lim\12)^(1/5), t1=p^5;forprime(q=2, sqrt(lim\t1), if(p==q, next);t2=t1*q^2;forprime(r=2, lim\t2, if(p==r||q==r, next);listput(v,t2*r)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 24 2011
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Python
from math import isqrt from sympy import primepi, primerange, integer_nthroot def A179691(n): def bisection(f,kmin=0,kmax=1): while f(kmax) > kmax: kmax <<= 1 kmin = kmax >> 1 while kmax-kmin > 1: kmid = kmax+kmin>>1 if f(kmid) <= kmid: kmax = kmid else: kmin = kmid return kmax def f(x): return n+x-sum(primepi(x//(p**5*q**2)) for p in primerange(integer_nthroot(x,5)[0]+1) for q in primerange(isqrt(x//p**5)+1))+sum(primepi(integer_nthroot(x//p**5,3)[0]) for p in primerange(integer_nthroot(x,5)[0]+1))+sum(primepi(isqrt(x//p**6)) for p in primerange(integer_nthroot(x,6)[0]+1))+sum(primepi(x//p**7) for p in primerange(integer_nthroot(x,7)[0]+1))-(primepi(integer_nthroot(x,8)[0])<<1) return bisection(f,n,n) # Chai Wah Wu, Mar 27 2025
Extensions
Name improved by M. F. Hasler, Jul 17 2019
Comments