cp's OEIS Frontend

A277624 Composite numbers which have a dominant prime factor. A prime factor p of n is dominant if floor(sqrt(p)) > (n/p).

%I A277624 #30 Sep 24 2023 10:40:16
%S A277624 22,26,34,38,46,51,57,58,62,69,74,82,86,87,93,94,106,111,116,118,122,
%T A277624 123,124,129,134,141,142,146,148,158,159,164,166,172,177,178,183,185,
%U A277624 188,194,201,202,205,206,212,213,214,215,218,219,226,235,236,237,244
%N A277624 Composite numbers which have a dominant prime factor. A prime factor p of n is dominant if floor(sqrt(p)) > (n/p).
%C A277624 From _David A. Corneth_, Oct 26 2016 and Oct 27 2016: (Start)
%C A277624 Numbers of the form k * p where p > (k + 1)^2 and p prime and k > 1.
%C A277624 If n has a dominant prime factor, it's A006530(n).
%C A277624 All primes p > 4 have the property that floor(sqrt(A006530(p))) = floor(sqrt(p)) > (p/A006530(p)) = 1.
%C A277624 A063763 is a supersequence.
%C A277624 (End)
%H A277624 Chai Wah Wu, <a href="/A277624/b277624.txt">Table of n, a(n) for n = 1..10000</a>
%F A277624 Conjecture: A092487(a(n)) = A006530(a(n)). - _David A. Corneth_, Oct 27 2016
%e A277624 133230 is in this sequence because 133230 = 2*3*5*4441 and 2*3*5 = 30 < 66 = floor(sqrt(4441)).
%p A277624 is_a := proc(n) max(numtheory:-factorset(n)):
%p A277624 not isprime(n) and floor(sqrt(%)) > (n/%) end:
%p A277624 select(is_a, [$1..244]);
%t A277624 Select[Select[Range@ 244, CompositeQ], Function[n, Total@ Boole@ Map[Function[p, Floor@ Sqrt@ p > n/p], FactorInteger[n][[All, 1]]] > 0]] (* _Michael De Vlieger_, Oct 27 2016 *)
%o A277624 (Python)
%o A277624 from sympy import primefactors
%o A277624 from gmpy2 import is_prime, isqrt
%o A277624 A277624_list = []
%o A277624 for n in range(2,10**3):
%o A277624     if not is_prime(n):
%o A277624         for p in primefactors(n):
%o A277624             if isqrt(p)*p > n:
%o A277624                 A277624_list.append(n)
%o A277624                 break # _Chai Wah Wu_, Oct 25 2016
%o A277624 (PARI) upto(n) = my(l=List()); for(k=2, sqrtnint(n, 3), forprime(p=(k+1)^2, n\k, listput(l,k*p))); listsort(l); l
%o A277624 is(n) = if(!isprime(n)&&n>1, f=factor(n)[, 1];sqrtint(f[#f]) > n/f[#f], 0) \\ _David A. Corneth_, Oct 26 2016
%Y A277624 Cf. A006530, A063763.
%K A277624 nonn,easy
%O A277624 1,1
%A A277624 _Peter Luschny_, Oct 24 2016