A053626 a(n) is the smallest positive integer k such that harmonic mean of n and k is an integer.

1, 2, 3, 4, 5, 2, 7, 8, 9, 10, 11, 4, 13, 14, 3, 16, 17, 6, 19, 5, 21, 22, 23, 8, 25, 26, 27, 4, 29, 6, 31, 32, 33, 34, 14, 12, 37, 38, 39, 10, 41, 7, 43, 44, 5, 46, 47, 16, 49, 50, 51, 52, 53, 18, 55, 8, 57, 58, 59, 12, 61, 62, 18, 64, 65, 6, 67, 68, 69, 28, 71, 9, 73, 74, 15, 76

Offset

1,2

Comments

If a(n) <> n, then n is in A005279.

a(n) is the smallest positive integer k such that n + k divides n^2 + k^2. - Altug Alkan, Mar 29 2018

Links

Altug Alkan, Table of n, a(n) for n = 1..10000

Wikipedia, Harmonic mean -- Two numbers

Example

a(6) = 2 because harmonic mean of 6 and 2 is 3 which is an integer and harmonic mean of 6 and 1 is 12/7 which is not an integer.

Mathematica

Array[If[Count[Partition[Divisors[#], 2, 1], _?(#2 < 2 #1 & @@ # &)] == 0, #, Block[{k = 1}, While[! IntegerQ@ HarmonicMean@{k, #}, k++]; k]] &, 76] (* Michael De Vlieger, Apr 05 2018 *)

Prog

(PARI) a(n) = {my(k=1); while((2*n*k) % (n+k) != 0, k++); k; } \\ Altug Alkan, Mar 29 2018

Crossrefs

Cf. A005279.

Sequence in context: A162961 A145255 A344758 * A348990 A348968 A333696

Adjacent sequences: A053623 A053624 A053625 * A053627 A053628 A053629

Keyword

nonn,easy

Author

Henry Bottomley, Mar 20 2000

Extensions

Name edited by Altug Alkan, Mar 29 2018

Status

approved