OFFSET
1,1
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
OEIS Wiki, Numbers with same prime signature.
Will Nicholes, Prime Signatures
FORMULA
Sum_{n>=1} 1/a(n) = P(2)*P(7) - P(9) = A085548 * A085967 - A085969 = 0.001741..., where P is the prime zeta function. - Amiram Eldar, Jul 06 2020
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, 2]
do od; k
end:
seq (a(n), n=1..32); # Alois P. Heinz, Jan 23 2011
MATHEMATICA
f[n_]:=Sort[Last/@FactorInteger[n]]=={2, 7}; Select[Range[10^6], f]
PROG
(PARI) list(lim)=my(v=List(), t); forprime(p=2, (lim\4)^(1/7), t=p^7; forprime(q=2, sqrt(lim\t), if(p==q, next); listput(v, t*q^2))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 20 2011
(Python)
from math import isqrt
from sympy import primepi, integer_nthroot, primerange
def A179689(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(isqrt(x//p**7)) for p in primerange(integer_nthroot(x, 7)[0]+1))+primepi(integer_nthroot(x, 9)[0])
return bisection(f, n, n) # Chai Wah Wu, Feb 21 2025
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Vladimir Joseph Stephan Orlovsky, Jul 24 2010
EXTENSIONS
Title edited by Daniel Forgues, Jan 22 2011
STATUS
approved