OFFSET
1,2
COMMENTS
Products of two noncomposite numbers. - Juri-Stepan Gerasimov, Apr 15 2010
Also, numbers with permutations of all divisors only with coprime adjacent elements: A109810(a(n)) > 0. - Reinhard Zumkeller, May 24 2010
A060278(a(n)) = 0. - Reinhard Zumkeller, Apr 05 2013
1 together with numbers k such that sigma(k) + phi(k) - d(k) = 2k - 2. - Wesley Ivan Hurt, May 03 2015
Products of two not necessarily distinct terms of A008578 (the same relation between A000040 and A001358). - Flávio V. Fernandes, May 28 2021
LINKS
Felix Fröhlich, Table of n, a(n) for n = 1..10000 (first 1000 terms from Reinhard Zumkeller)
Andreas Weingartner, Uniform distribution of alpha*n modulo one for a family of integer sequences, arXiv:2303.16819 [math.NT], 2023.
MAPLE
with(numtheory): A037143:=n->`if`(bigomega(n)<3, n, NULL): seq(A037143(n), n=1..200); # Wesley Ivan Hurt, May 03 2015
MATHEMATICA
Select[Range[120], PrimeOmega[#] <= 2 &] (* Ivan Neretin, Aug 16 2015 *)
PROG
(Haskell)
a037143 n = a037143_list !! (n-1)
a037143_list = 1 : merge a000040_list a001358_list where
merge xs'@(x:xs) ys'@(y:ys) =
if x < y then x : merge xs ys' else y : merge xs' ys
-- Reinhard Zumkeller, Dec 18 2012
(PARI) is(n)=bigomega(n)<3 \\ Charles R Greathouse IV, Apr 29 2015
(Python)
from math import isqrt
from sympy import primepi, primerange
def A037143(n):
def f(x): return int(n-2+x-primepi(x)-sum(primepi(x//k)-a for a, k in enumerate(primerange(isqrt(x)+1))))
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
A101040(a(n))=1 for n>1.
Subsequence of A037144. - Reinhard Zumkeller, May 24 2010
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Henry Bottomley, Aug 15 2001
STATUS
approved