| 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99
(list)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
These are the natural numbers with an even number of divisors. The number of divisors is odd for the complementary sequence, the squares (sequence A000290), and the numbers for which the number of divisors is divisible by 3 is sequence A059269. - Ola Veshta (olaveshta(AT)my-deja.com), Apr 04 2001
|
|
REFERENCES
|
M. A. Nyblom, Some curious sequences ..., Am. Math. Monthly 109 (#6, 200), 559-564.
A. J. dos Reis and D. M. Silberger, Generating nonpowers by formula, Math. Mag., 63 (1990), 53-55.
|
|
LINKS
|
S. R. Finch, Class number theory
E. W. Weisstein, Link to a section of The World of Mathematics (1)
E. W. Weisstein, Link to a section of The World of Mathematics (2)
|
|
FORMULA
|
a(n) = n + [1/2 + sqrt(n)].
Another formula: a(n) = n + [ sqrt( n + [ sqrt n ] ) ].
|
|
EXAMPLE
|
For example note that the squares 1, 4, 9, 16 are not included.
|
|
MAPLE
|
A000037 := n->n+floor(1/2+sqrt(n));
|
|
MATHEMATICA
|
f[n_] := (n + Floor[Sqrt[n + Floor[Sqrt[n]]]]); Table[ f[n], {n, 71}] (from Robert G. Wilson v Sep 24 2004)
|
|
PROGRAM
|
(PARI) a(n)=if(n<0, 0, n+(1+sqrtint(4*n))\2)
|
|
CROSSREFS
|
Cf. A007412, A000005, A000290, A059269.
Equals A000194(n) + n.
Sequence in context: A028729 A072099 A046841 this_sequence A028761 A028809 A028785
Adjacent sequences: A000034 A000035 A000036 this_sequence A000038 A000039 A000040
|
|
KEYWORD
|
easy,nonn,nice
|
|
AUTHOR
|
njas, Simon Plouffe (plouffe(AT)math.uqam.ca)
|
|
