A179698 Numbers of the form p^4*q^3*r where p, q, and r are distinct primes.

2160, 3024, 3240, 4536, 4752, 5616, 6000, 7128, 7344, 8208, 8424, 9936, 11016, 12312, 12528, 13392, 14000, 14904, 15000, 15984, 16464, 17712, 18576, 18792, 20088, 20250, 20304, 22000, 22896, 23976, 25488, 26000, 26352, 26568, 27440

Offset

1,1

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

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={1, 3, 4}; Select[Range[30000], f]

Prog

(PARI) list(lim)=my(v=List(), t1, t2); forprime(p=2, (lim\24)^(1/4), t1=p^4; forprime(q=2, (lim\t1)^(1/3), if(p==q, next); t2=t1*q^3; 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
(Python)
from sympy import primepi, primerange, integer_nthroot
def A179698(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**4*q**3)) for p in primerange(integer_nthroot(x, 4)[0]+1) for q in primerange(integer_nthroot(x//p**4, 3)[0]+1))+sum(primepi(integer_nthroot(x//p**4, 4)[0]) for p in primerange(integer_nthroot(x, 4)[0]+1))+sum(primepi(integer_nthroot(x//p**5, 3)[0]) for p in primerange(integer_nthroot(x, 5)[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 28 2025

Crossrefs

Sequence in context: A252126 A192771 A152963 * A075702 A389340 A205629

Adjacent sequences: A179695 A179696 A179697 * A179699 A179700 A179701

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 24 2010

Status

approved