OFFSET
1,1
COMMENTS
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
Will Nicholes, List of Prime Signatures
EXAMPLE
180 = 2^2 * 3^2 * 5, 252 = 2^2 * 3^2 * 7, 300 = 2^2 * 3 * 5^2, ...
MATHEMATICA
f[n_]:=Sort[Last/@FactorInteger[n]]=={1, 2, 2}; Select[Range[3000], f]
PROG
(PARI) list(lim)=my(v=List(), t); forprime(p=2, sqrt(lim\12), forprime(q=p+1, sqrt(lim\p^2\2), t=(p*q)^2; forprime(r=2, lim\t, if(p==r||q==r, next); listput(v, t*r)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 19 2011
(Python)
from math import isqrt
from sympy import primepi, primerange, integer_nthroot
def A179643(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:=isqrt(x//r))))+(t*(t-1)>>1)-sum(primepi(y//k) for k in primerange(1, s+1)) for r in primerange(x+1))+sum(primepi(isqrt(x//p**3)) for p in primerange(integer_nthroot(x, 3)[0]+1))-primepi(integer_nthroot(x, 5)[0])
return bisection(f, n, n) # Chai Wah Wu, Mar 27 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Jul 21 2010
STATUS
approved