

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
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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



FORMULA



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(k1) + 1)^2  k), print1(k, ", ")) ))} \\ Andrew Howroyd, Aug 12 2018


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



