

A038389


Let f(n) be the smallest number such that the arithmetic mean (A) and geometric mean (G) of n and f(n) are both integers; sequence gives A values.


3



1, 2, 3, 4, 5, 6, 7, 5, 5, 10, 11, 12, 13, 14, 15, 10, 17, 10, 19, 20, 21, 22, 23, 15, 13, 26, 15, 28, 29, 30, 31, 17, 33, 34, 35, 20, 37, 38, 39, 25, 41, 42, 43, 44, 25, 46, 47, 30, 25, 26, 51, 52, 53, 30, 55, 35, 57, 58, 59, 60, 61, 62, 35, 34, 65, 66, 67, 68, 69, 70, 71, 37, 73, 74, 39, 76, 77, 78
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OFFSET

1,2


COMMENTS

It is the average of A038387 with n, both of which are multiplicative.  Christian G. Bower, May 16 2005
However, this sequence is not multiplicative. The first nonmultiplicative term is a(72) = 37 which is not multiplicative since a(8)*a(9) = 5*5 = 25.  Andrew Howroyd, Feb 12 2018


LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000


MATHEMATICA

Table[k = 1; While[Nand @@ IntegerQ /@ {a = (n + k)/2, Sqrt[n*k]}, k++]; a, {n, 78}] (* Jayanta Basu, Jul 14 2013 *)


PROG

(PARI) a(n)={for(k=1, n, if((n+k)%2==0 && issquare(n*k), return((n+k)/2)))} \\ Andrew Howroyd, Feb 12 2018


CROSSREFS

Cf. A038387, A038388.
Sequence in context: A355261 A353897 A348262 * A058223 A245355 A307785
Adjacent sequences: A038386 A038387 A038388 * A038390 A038391 A038392


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


STATUS

approved



