A361799 Numbers which cannot be expressed as i^2 + j*k with i >= j >= k >= 0.

3, 7, 14, 21, 23, 43, 47, 62, 75, 119, 134, 138, 167, 215, 318, 398, 566, 1487

Offset

1,1

Comments

Is this list infinite?

a(19) > 3.5 * 10^8. - Delbert L. Johnson, May 04 2024

Links

Table of n, a(n) for n=1..18.

Math Pickle, Big Square Mini Mathematical Universe, YouTube video.

Example

14 is a term because there are no solutions to 14 = i^2 + j*k with i >= j >= k >= 0. Specifically 14 = 3^2 + 5*1 is not a solution because 5 > 3.
117 is not a term because 117 = 9^2 + 6*6.
118 is not a term because 118 = 10^2 + 9*2 (also 118 = 10^2 + 6*3).

Prog

(PARI) isok(n)={for(k=sqrtint(n\2), sqrtint(n), my(r=n-k^2); if(r==0, return(0)); fordiv(r, d, if(d<=k && r/d<=k, return(0)))); 1}
select(isok, [1..2000]) \\ Andrew Howroyd, Mar 24 2023

Crossrefs

Sequence in context: A310273 A310274 A310275 * A310276 A310277 A354957

Adjacent sequences: A361796 A361797 A361798 * A361800 A361801 A361802

Keyword

nonn,more

Author

Gordon Hamilton, Mar 24 2023

Extensions

a(11)-a(18) from Andrew Howroyd, Mar 24 2023

Status

approved