OFFSET
1,1
COMMENTS
Also numbers k such that k is in A005279 but none of the proper divisors of k are.
All terms k are composites; if k is prime then it's not in A005279 hence not here. If k = m * t and t < m < 2*t then m and t are coprime. If g = gcd(t, m) > 1 then the integer k / g^2 is in A005279. If there is some term u*t where with u > 2*t and gcd(u, t) = 1 then there is some m * t' with gcd(m, t') = 1 such that m*t' | t * u and t * u wouldn't be in the sequence. if u = 2*t then gcd(u, t) = t which can't happen.
It could be that both m and t are composite, for example, t = 53^2 and m = 5^5 gives the term 53^2 * 5^5.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
A301989(a(n)) = 1.
PROG
(PARI) is005279(n) = my(d=divisors(n)); for(i=3, #d, if(d[i]<2*d[i-1], return(1))); 0;
is(n) = if (is005279(n), d = divisors(n); for (k=1, #d-1, if (is005279(d[k]), return (0)); ); return(1); ); \\ Altug Alkan, Apr 14 2018
upto(n) = {my(res = List()); for(i = 2, sqrtint(n), for(j = i+1, min(2 * i - 1, n\i), if(gcd(i, j) == 1, if(is(i*j), listput(res, i*j))))); listsort(res); return(res)} \\ David A. Corneth, Apr 15 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
David A. Corneth, Mar 31 2018
STATUS
approved