OFFSET
1,1
COMMENTS
Subsequence of A030628.
FORMULA
a(n) ~ kn log n with k = 1/P(4) = 1/A085964 = 12.98817.... - Charles R Greathouse IV, Feb 23 2017
MATHEMATICA
f[n_]:=Sort[Last/@FactorInteger[n]]=={1, 4}; Select[Range[10000], f] (* Vladimir Joseph Stephan Orlovsky, May 03 2011 *)
max = 500000; A178739 = DeleteCases[Union[Table[Prime[p] Prime[q]^4 Boole[p != q], {p, PrimePi[max/16]}, {q, PrimePi[max/2]}]], 0]; Take[A178739, 50] (* Alonso del Arte, Aug 05 2012 *)
PROG
(PARI) list(lim)=my(v=List(), t); forprime(p=2, (lim\2)^(1/4), t=p^4; forprime(q=2, lim\t, if(p==q, next); listput(v, t*q))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 20 2011
(Python)
from sympy import primepi, primerange, integer_nthroot
def A178739(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) for p in primerange(integer_nthroot(x, 4)[0]+1))+primepi(integer_nthroot(x, 5)[0])
return bisection(f, n, n) # Chai Wah Wu, Feb 21 2025
CROSSREFS
KEYWORD
easy,nonn,changed
AUTHOR
Will Nicholes, Jun 08 2010
STATUS
approved