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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.
0
15, 30, 35, 45, 55, 60, 70, 75, 77, 90, 91, 105, 110, 119, 120, 135, 140, 143, 150, 154, 165, 175, 180, 182, 187, 195, 209, 210, 220, 221, 225, 231, 238, 240, 245, 247, 253, 255, 270, 273, 275, 280, 285, 286, 299, 300, 308, 315, 319, 323, 330, 341, 345, 350, 357, 360, 364, 374, 375, 377
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
Cf. A289484.
Sequence in context: A051967 A162592 A239247 * A079877 A215951 A060700
KEYWORD
nonn
AUTHOR
STATUS
approved