The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A317518 Highly composite numbers k such that ceiling(sqrt(k))^2 - k is a square. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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
LINKS
Michael De Vlieger, Concordance of A317518 and A002182 listing a(n) and positions of a(n) in A002182, along with the qualifying square roots.
FORMULA
Intersection of A002182 and A256173. - Andrew Howroyd, Aug 12 2018
EXAMPLE
1, 4, and 36 are square. 24, 48, 120, 360, 840, 1680, and 5040 are all 1 less than a square.
PROG
(PARI) {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
CROSSREFS
Sequence in context: A218391 A297568 A353795 * A307763 A071228 A304077
KEYWORD
nonn
AUTHOR
Vaughn R Tiffany, Jul 30 2018
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 12:18 EDT 2024. Contains 372630 sequences. (Running on oeis4.)