Vaughn R Tiffany - cp's OEIS frontend

User: Vaughn R Tiffany

Vaughn R Tiffany has authored 1 sequences.

A317518 Highly composite numbers k such that ceiling(sqrt(k))^2 - k is a square.

1, 4, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560, 10080, 15120, 20160, 25200, 27720, 45360, 50400, 55440, 83160, 110880, 166320, 221760, 277200, 332640, 554400

Offset: 1

Vaughn R Tiffany, Jul 30 2018

nonn

Up to 17297280 only the highly composite numbers 2, 6, 498960, 1081080, and 4324320 don't qualify. I have tested all up to that point.

Conjecture: this sequence is finite, with a(120) = 7675044034503567507122937600 as its final term. - Jon E. Schoenfield, Aug 12 2018

			1, 4, and 36 are square. 24, 48, 120, 360, 840, 1680, and 5040 are all 1 less than a square.

Michael De Vlieger, Table of n, a(n) for n = 1..120
Michael De Vlieger, Concordance of A317518 and A002182 listing a(n) and positions of a(n) in A002182, along with the qualifying square roots.

Cf. A002182, A256173.

{my(r=0); for(k=1, 5e5, if(numdiv(k)>r, r=numdiv(k); if(issquare((sqrtint(k-1) + 1)^2 - k), print1(k, ", ")) ))} \\ Andrew Howroyd, Aug 12 2018

Intersection of A002182 and A256173. - Andrew Howroyd, Aug 12 2018

cp's OEIS Frontend

User: Vaughn R Tiffany

A317518 Highly composite numbers k such that ceiling(sqrt(k))^2 - k is a square.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula