

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
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OFFSET

2,2


COMMENTS

Or, smallest b such that 1/n + 1/c = 1/b has integer solutions.
Largest b is (n1) since 1/n + 1/(n(n1)) = 1/(n1).
a(n) = smallest k such that k*n/(kn) is an integer.  Derek Orr, May 29 2014


LINKS



FORMULA



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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



