OFFSET
1,1
COMMENTS
Divisible by exactly 5 prime powers (not including 1).
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Almost Prime
FORMULA
Product p_i^e_i with sum e_i = 5.
a(n) ~ 24n log n/(log log n)^4. - Charles R Greathouse IV, Mar 20 2013
a(n) = A078840(5,n). - R. J. Mathar, Jan 30 2019
MATHEMATICA
Select[Range[300], Plus @@ Last /@ FactorInteger[ # ] == 5 &] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2008 *)
PROG
(PARI) is(n)=bigomega(n)==5 \\ Charles R Greathouse IV, Mar 20 2013
(Python)
from math import isqrt
from sympy import primepi, primerange, integer_nthroot
def A014614(n):
def f(x): return int(n+x-sum(primepi(x//(k*m*r*s))-d for a, k in enumerate(primerange(integer_nthroot(x, 5)[0]+1)) for b, m in enumerate(primerange(k, integer_nthroot(x//k, 4)[0]+1), a) for c, r in enumerate(primerange(m, integer_nthroot(x//(k*m), 3)[0]+1), b) for d, s in enumerate(primerange(r, isqrt(x//(k*m*r))+1), c)))
m, k = n, f(n)
while m != k:
m, k = k, f(k)
return m # Chai Wah Wu, Aug 17 2024
CROSSREFS
Sequences listing r-almost primes, that is, the n such that A001222(n) = r: A000040 (r = 1), A001358 (r = 2), A014612 (r = 3), A014613 (r = 4), this sequence (r = 5), A046306 (r = 6), A046308 (r = 7), A046310 (r = 8), A046312 (r = 9), A046314 (r = 10), A069272 (r = 11), A069273 (r = 12), A069274 (r = 13), A069275 (r = 14), A069276 (r = 15), A069277 (r = 16), A069278 (r = 17), A069279 (r = 18), A069280 (r = 19), A069281 (r = 20). - Jason Kimberley, Oct 02 2011
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu) and Patrick De Geest, Jun 15 1998
STATUS
approved