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 A063428 a(n) is the smallest positive integer of the form n*k/(n+k). 11
 1, 2, 2, 4, 2, 6, 4, 6, 5, 10, 3, 12, 7, 6, 8, 16, 6, 18, 4, 12, 11, 22, 6, 20, 13, 18, 12, 28, 5, 30, 16, 22, 17, 10, 9, 36, 19, 26, 8, 40, 6, 42, 22, 18, 23, 46, 12, 42, 25, 34, 26, 52, 18, 30, 7, 38, 29, 58, 10, 60, 31, 14, 32, 40, 22, 66, 34, 46, 20, 70, 8, 72, 37, 30, 38, 28, 26 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS Or, smallest b such that 1/n + 1/c = 1/b has integer solutions. Largest b is (n-1) since 1/n + 1/(n(n-1)) = 1/(n-1). a(n) = smallest k such that k*n/(k-n) is an integer. - Derek Orr, May 29 2014 LINKS Harry J. Smith, Table of n, a(n) for n = 2..1000 FORMULA a(n) = n*A063427(n)/(n + A063427(n)) = 2n - A063649(n). If n is prime a(n) = n - 1. - Benoit Cloitre, Dec 31 2001 EXAMPLE a(6) = 2 because 6*3/(6+3) = 2 is the smallest integer of the form 6*k/(6+k). a(10) = 5 since 1/10 + 1/10 = 1/5, 1/10 + 1/15 = 1/6, 1/10 + 1/40 = 1/8, 1/10 + 1/90 = 1/9 and so the first sum provides the value. MATHEMATICA spi[n_]:=Module[{k=1}, While[!IntegerQ[(n*k)/(n+k)], k++]; (n*k)/(n+k)]; Array[ spi, 80, 2] (* Harvey P. Dale, May 05 2022 *) PROG (PARI) a(n)={my(k=1); if(n>1, while (n*k%(n + k), k++); n*k/(n + k))} \\ Harry J. Smith, Aug 20 2009 CROSSREFS Cf. A018892, A063427, A127730, A063647, A063648, A063649, A066092. Sequence in context: A122645 A122646 A028496 * A133439 A234649 A072300 Adjacent sequences: A063425 A063426 A063427 * A063429 A063430 A063431 KEYWORD nonn AUTHOR Henry Bottomley, Jul 19 2001 EXTENSIONS New description from Benoit Cloitre, Dec 31 2001 Entry revised by N. J. A. Sloane, Feb 13 2007 Definition revised by Franklin T. Adams-Watters, Aug 07 2009 STATUS approved

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Last modified December 6 09:20 EST 2023. Contains 367600 sequences. (Running on oeis4.)