OFFSET
1,1
COMMENTS
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.
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.
EXAMPLE
6 = 2*3 is not in the sequence since 2^3 < 3^2.
15 = 3*5 is in the sequence because 3^3 > 5^2.
MAPLE
isA291045 := proc(n)
local pdivs, i, j;
pdivs := sort(convert(numtheory[factorset](n), list)) ;
for i from 1 to nops(pdivs)-1 do
for j from i+1 to nops(pdivs) do
if op(i, pdivs)^3 > op(j, pdivs)^2 then
return true;
end if;
end do:
end do:
false;
end proc:
for n from 1 to 400 do
if isA291045(n) then
printf("%d, ", n) ;
end if;
end do: # R. J. Mathar, Sep 04 2017
MATHEMATICA
Select[Range@ 400, AnyTrue[Partition[FactorInteger[#][[All, 1]], 2, 1], #1^3 > #2^2 & @@ # &] &] (* Michael De Vlieger, Aug 17 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Richard Locke Peterson, Aug 16 2017
STATUS
approved