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URL: https://oeis.org/A063717

⇱ A063717 - OEIS

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A063717
a(n) is the greatest divisor of n^2 that is less than n.
4
1, 1, 2, 1, 4, 1, 4, 3, 5, 1, 9, 1, 7, 9, 8, 1, 12, 1, 16, 9, 11, 1, 18, 5, 13, 9, 16, 1, 25, 1, 16, 11, 17, 25, 27, 1, 19, 13, 32, 1, 36, 1, 22, 27, 23, 1, 36, 7, 25, 17, 26, 1, 36, 25, 49, 19, 29, 1, 50, 1, 31, 49, 32, 25, 44, 1, 34, 23, 50, 1, 64, 1, 37, 45, 38, 49, 52, 1, 64, 27, 41
OFFSET
2,3
COMMENTS
Smaller of two distinct numbers with minimum sum whose geometric mean is n. E.g., a(12) = 9 as 12^2 = 144 = 1*144 = 2*72 = 3*48 = 4*36 = 6*24 = 8*18 = 9*16, etc. - Amarnath Murthy, Feb 15 2003
LINKS
EXAMPLE
a(45)=27 because set of divisors of 45^2 is {1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 405, 675, 2025} and the greatest element of the set less than 45 is 27.
MAPLE
with(numtheory): for n from 2 to 200 do a := divisors(n^2): b := a[(tau(n^2)-1)/2]: printf(`%d, `, b); od:
MATHEMATICA
f[n_] := Module[{dn2 = Divisors[n^2]}, Last[Take[dn2, {1, Flatten[Position[dn2, n]][[ 1]] - 1}]]]; Table[f[i], {i, 2, 85}]
Table[Select[Divisors[n^2], #<n&][[-1]], {n, 2, 100}] (* Harvey P. Dale, Apr 23 2016 *)
PROG
(PARI) { for (n=2, 1000, d=divisors(n^2); write("b063717.txt", n, " ", d[length(d)\2]) ) } \\ Harry J. Smith, Aug 28 2009
CROSSREFS
A063649(n) = n + a(n), A063718(n) = n^2/A063717(n), A063428(n) = n - a(n).
Cf. A063718.
Sequence in context: A321437 A319711 A319713 * A024994 A243329 A051953
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Aug 12 2001
STATUS
approved