OFFSET
1,2
COMMENTS
Also numbers such that exist permutations of all proper divisors only with coprime adjacent elements: A178254(a(n))>0. - Reinhard Zumkeller, May 24 2010
LINKS
Klaus Brockhaus, Table of n, a(n) for n = 1..10000
FORMULA
a(n) ~ 2n log n/(log log n)^2. - Charles R Greathouse IV, Sep 14 2015
MATHEMATICA
Select[Range[100], PrimeOmega[#]<4&] (* Harvey P. Dale, Oct 15 2015 *)
PROG
(Magma) [ n: n in [1..86] | n eq 1 or &+[ t[2]: t in Factorization(n) ] le 3 ]; /* Klaus Brockhaus, Mar 20 2007 */
(PARI) is(n)=bigomega(n)<4 \\ Charles R Greathouse IV, Sep 14 2015
(Python)
from math import prod, isqrt
from sympy import primerange, integer_nthroot, primepi
def A037144(n):
def g(x, a, b, c, m): yield from (((d, ) for d in enumerate(primerange(b, isqrt(x//c)+1), a)) if m==2 else (((a2, b2), )+d for a2, b2 in enumerate(primerange(b, integer_nthroot(x//c, m)[0]+1), a) for d in g(x, a2, b2, c*b2, m-1)))
def f(x): return int(n+x-2-primepi(x)-sum(sum(primepi(x//prod(c[1] for c in a))-a[-1][0] for a in g(x, 0, 1, 1, i)) for i in range(2, 4)))
kmin, kmax = 1, 2
while f(kmax) >= kmax:
kmax <<= 1
while True:
kmid = kmax+kmin>>1
if f(kmid) < kmid:
kmax = kmid
else:
kmin = kmid
if kmax-kmin <= 1:
break
return kmax # Chai Wah Wu, Aug 23 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Reinhard Zumkeller, Mar 10 2006
More terms from Klaus Brockhaus, Mar 20 2007
STATUS
approved