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A324176 Integers k such that floor(sqrt(k)) + floor(sqrt(k/3)) divides k. 3
1, 2, 6, 15, 18, 24, 32, 36, 45, 55, 72, 78, 84, 98, 105, 112, 136, 144, 152, 180, 198, 220, 230, 275, 336, 390, 403, 462, 525, 540, 608, 663, 697, 756, 774, 792, 836, 855, 874, 940, 980, 1050, 1092, 1144, 1166, 1265, 1368, 1392, 1500, 1525, 1586, 1638, 1755, 1782, 1848, 1904 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence is infinite for the same reason that A324175 is: if x-1 > y > 1 satisfies x^2 - 3*y^2 = -2 (x=A001834(j), y=A001835(j+1), j>0), then x < 3*y. Let k = 3*y^2 + m. By the pigeonhole principle there exists a number m belonging to [0, 2*x - 2] such that x + y | 3*y^2 + m, so such a k is a term.

LINKS

Table of n, a(n) for n=1..56.

PROG

(PARI) is(n) = n%(floor(sqrt(n)) + floor(sqrt(n/3))) == 0;

CROSSREFS

Cf. A001834, A001835, A324175.

Sequence in context: A134891 A020947 A011777 * A294942 A227307 A129631

Adjacent sequences:  A324173 A324174 A324175 * A324177 A324178 A324179

KEYWORD

nonn

AUTHOR

Jinyuan Wang, Mar 08 2019

STATUS

approved

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Last modified June 4 10:43 EDT 2020. Contains 334825 sequences. (Running on oeis4.)