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 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, 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. 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 Cf. A002182, A256173. Sequence in context: A218391 A297568 A353795 * A307763 A071228 A304077 Adjacent sequences: A317515 A317516 A317517 * A317519 A317520 A317521 KEYWORD nonn AUTHOR Vaughn R Tiffany, Jul 30 2018 STATUS approved

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