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 A163520 a(n) is the least integer x such that n < x and the product n*x is divisible by an integer y where n < y < x. 0
 4, 6, 8, 9, 12, 12, 16, 15, 16, 18, 24, 20, 28, 24, 24, 25, 36, 28, 40, 30, 32, 36, 48, 35, 36, 42, 40, 40, 60, 42, 64, 45, 48, 54, 48, 49, 76, 60, 56, 54, 84, 56, 88, 60, 60, 72, 96, 63, 64, 66, 72, 70, 108, 70, 72, 72, 80, 90, 120, 77, 124, 96, 80, 81 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) is the smallest area of an integer-sided rectangle able to enclose without contact an integer-sided rectangle of area n. The enclosing rectangle has sides A033676(n)+1 and A033677(n)+1. See the first formula below. - Peter Munn, Apr 26 2019 LINKS Estonian Math Competitions 2008/2009, problem TS-6, pages 23-24 FORMULA a(n) = (A033676(n)+1) * (A033677(n)+1). a(n) = n + A033676(n) + A033677(n) + 1. a(n) = n + A063655(n) + 1. a(n^2) = (n+1)^2; a(n^2-n) = n^2 + n. a(p) = 2*(p+1) for p prime. EXAMPLE For example, a(6)=12 since 6*7 is not divisible by any number between 6 and 7, and 6*8 is not divisible by any number between 6 and 8, and 6*9 is not divisible by any number between 6 and 9, and 6*10 is not divisible by any number between 6 and 10, and 6*11 is not divisible by any number between 6 and 11, but 6*12 is divisible by 9 which is between 6 and 12. CROSSREFS Cf. A033676, A033677, A063655. Sequence in context: A202268 A084985 A068631 * A273546 A176539 A285256 Adjacent sequences:  A163517 A163518 A163519 * A163521 A163522 A163523 KEYWORD nonn AUTHOR Harmel Nestra (harmel.nestra(AT)ut.ee), Jul 30 2009 EXTENSIONS Formulas extended by Franklin T. Adams-Watters, Aug 06 2009 STATUS approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)