cp's OEIS Frontend

A291045 Numbers with prime factorization such that the cube of a lesser prime in the factorization is greater than the square of a greater prime in the factorization.

%I A291045 #10 Sep 04 2017 12:54:33
%S A291045 15,30,35,45,55,60,70,75,77,90,91,105,110,119,120,135,140,143,150,154,
%T A291045 165,175,180,182,187,195,209,210,220,221,225,231,238,240,245,247,253,
%U A291045 255,270,273,275,280,285,286,299,300,308,315,319,323,330,341,345,350,357,360,364,374,375,377
%N A291045 Numbers with prime factorization such that the cube of a lesser prime in the factorization is greater than the square of a greater prime in the factorization.
%C A291045 Definition rephrased: if n is a number with prime divisors p and q with p < q but p^3 > q^2, then n will be in the sequence, otherwise, not.
%C A291045 Sequence is a superclosed semigroup; that is, if s is in the sequence and x is any number, then x*s is in the sequence: if s in the sequence, there are primes p,q dividing s with p < q, p^3 > q^2, so p and q would also divide x*s.
%e A291045 6 = 2*3 is not in the sequence since 2^3 < 3^2.
%e A291045 15 = 3*5 is in the sequence because 3^3 > 5^2.
%p A291045 isA291045 := proc(n)
%p A291045     local pdivs,i,j;
%p A291045     pdivs := sort(convert(numtheory[factorset](n),list)) ;
%p A291045     for i from 1 to nops(pdivs)-1 do
%p A291045     for j from i+1 to nops(pdivs) do
%p A291045         if op(i,pdivs)^3 > op(j,pdivs)^2 then
%p A291045             return true;
%p A291045         end if;
%p A291045     end do:
%p A291045     end do:
%p A291045     false;
%p A291045 end proc:
%p A291045 for n from 1 to 400 do
%p A291045     if isA291045(n) then
%p A291045         printf("%d,",n) ;
%p A291045     end if;
%p A291045 end do: # _R. J. Mathar_, Sep 04 2017
%t A291045 Select[Range@ 400, AnyTrue[Partition[FactorInteger[#][[All, 1]], 2, 1], #1^3 > #2^2 & @@ # &] &] (* _Michael De Vlieger_, Aug 17 2017 *)
%Y A291045 Cf. A289484.
%K A291045 nonn
%O A291045 1,1
%A A291045 _Richard Locke Peterson_, Aug 16 2017