A179696 Numbers with prime signature {7,1,1}, i.e., of form p^7*q*r with p, q and r distinct primes.

1920, 2688, 4224, 4480, 4992, 6528, 7040, 7296, 8320, 8832, 9856, 10880, 11136, 11648, 11904, 12160, 14208, 14720, 15232, 15744, 16512, 17024, 18048, 18304, 18560, 19840, 20352, 20608, 21870, 22656, 23424, 23680, 23936, 25728, 25984, 26240, 26752, 27264

Offset

1,1

Links

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

Will Nicholes List of Prime Signatures

OEIS Wiki, Numbers with same prime signature.

Maple

a:= proc(n) option remember; local k;
      for k from 1+ `if` (n=1, 1, a(n-1))
        while sort (map (x-> x[2], ifactors(k)[2]), `>`)<>[7, 1, 1]
      do od; k
    end:
seq (a(n), n=1..40); # Alois P. Heinz, Jan 23 2011

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={1, 1, 7}; Select[Range[30000], f]

Prog

(PARI) list(lim)=my(v=List(), t1, t2); forprime(p=2, (lim\6)^(1/7), t1=p^7; forprime(q=2, lim\t1, if(p==q, next); t2=t1*q; forprime(r=q+1, lim\t2, if(p==r, next); listput(v, t2*r)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 20 2011
(Python)
from math import isqrt
from sympy import primerange, primepi, integer_nthroot
def A179696(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**7)))+(t*(t-1)>>1)-sum(primepi(y//k) for k in primerange(1, s+1)) for r in primerange(integer_nthroot(x, 7)[0]+1))+sum(primepi(x//p**8) for p in primerange(integer_nthroot(x, 8)[0]+1))-primepi(integer_nthroot(x, 9)[0])
    return bisection(f, n, n) # Chai Wah Wu, Mar 27 2025

Crossrefs

Cf. A006881, A007304, A065036, A085986, A085987, A092759, A178739, A179642, A179643, A179644, A179645, A179646, A179664, A179665, A179666, A179667, A179668, A179669, A179670, A179671, A179672, A179688, A179689, A179690, A179691, A179692, A179693, A179694, A179695.

Sequence in context: A309031 A361347 A077087 * A249840 A061374 A282474

Adjacent sequences: A179693 A179694 A179695 * A179697 A179698 A179699

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 24 2010

Extensions

Title edited by Daniel Forgues, Jan 22 2011

Status

approved