A179667 Products of the 5th power of a prime and 2 distinct primes (p^5*q*r).

480, 672, 1056, 1120, 1248, 1632, 1760, 1824, 2080, 2208, 2430, 2464, 2720, 2784, 2912, 2976, 3040, 3402, 3552, 3680, 3808, 3936, 4128, 4256, 4512, 4576, 4640, 4960, 5088, 5152, 5346, 5664, 5856, 5920, 5984, 6318, 6432, 6496, 6560, 6688, 6816, 6880

Offset

1,1

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Will Nicholes, Prime Signatures

Index to sequences related to prime signature

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={1, 1, 5}; Select[Range[10000], f]

Prog

(PARI) list(lim)=my(v=List(), t); forprime(p=2, (lim\6)^(1/5), forprime(q=2, sqrt(lim\p^5), if(p==q, next); t=p^5*q; forprime(r=q+1, lim\t, if(p==r, next); listput(v, t*r)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 20 2011
(Python)
from math import isqrt
from sympy import primepi, primerange, integer_nthroot
def A179667(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((t:=primepi(s:=isqrt(y:=x//r**5)))+(t*(t-1)>>1)-sum(primepi(y//k) for k in primerange(1, s+1)) for r in primerange(integer_nthroot(x, 5)[0]+1))+sum(primepi(x//p**6) for p in primerange(integer_nthroot(x, 6)[0]+1))-primepi(integer_nthroot(x, 7)[0])
    return bisection(f, n, n) # Chai Wah Wu, Mar 27 2025

Crossrefs

Sequence in context: A019287 A258551 A257415 * A108876 A293187 A206200

Adjacent sequences: A179664 A179665 A179666 * A179668 A179669 A179670

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 23 2010

Status

approved