proposed

approved

editing

proposed

return kmax # Chai Wah Wu, Aug 23 2024

(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

approved

editing

(MAGMAMagma) [ n: n in [1..86] | n eq 1 or &+[ t[2]: t in Factorization(n) ] le 3 ]; /* Klaus Brockhaus, Mar 20 2007 */

editing

approved

Select[Range[100], PrimeOmega[#]<4&] (* Harvey P. Dale, Oct 15 2015 *)

approved

editing

editing

approved

Also numbers such that exist permutations of all proper divisors only with coprime adjacent elements: A178254(a(n))>0. [From _- _Reinhard Zumkeller_, May 24 2010]

Klaus Brockhaus, <a href="/A037144/b037144.txt">Table of n, a(n) for n = 1..10000</a>

a(n) ~ 2n log n/(log log n)^2. - Charles R Greathouse IV, Sep 14 2015

(PARI) is(n)=bigomega(n)<4 \\ Charles R Greathouse IV, Sep 14 2015

A037143 is a subsequence.

A037143 is a subsequence. [From Reinhard Zumkeller, May 24 2010]

approved

editing

Complement of A033987: A001222(a(n))<=3; A117358(a(n))=1. - _Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, Mar 10 2006

Also numbers such that exist permutations of all proper divisors only with coprime adjacent elements: A178254(a(n))>0. [From _Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, May 24 2010]

A037143 is a subsequence. [From _Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, May 24 2010]

More terms from _Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, Mar 10 2006