|
| |
|
|
A039955
|
|
Squarefree numbers congruent to 1 mod 4.
|
|
7
|
|
|
|
1, 5, 13, 17, 21, 29, 33, 37, 41, 53, 57, 61, 65, 69, 73, 77, 85, 89, 93, 97, 101, 105, 109, 113, 129, 133, 137, 141, 145, 149, 157, 161, 165, 173, 177, 181, 185, 193, 197, 201, 205, 209, 213, 217, 221, 229, 233, 237, 241, 249, 253, 257, 265, 269
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
The subsequence of primes is A002144.
The subsequence of semiprimes (intersection with A001358) begins: 21, 33, 57, 65, 69, 77, 85, 93, 129, 133, 141, 145, 161, 177, 185, 201, 205, 209, 213, 217, 221, 237, 249, 253, 265.
The subsequence with more than two prime factors (intersection with A033942) begins: 105 = 3 * 5 * 7, 165 = 3 * 5 * 11, 273, 285, 345, 357, 385, 429, 465. [Jonathan Vos Post, Feb 19 2011].
Except for a(1) = 1 these are the squarefree members of A079896 (i.e., squarefree determinants D of indefinite binary quadratic forms). - Wolfdieter Lang, Jun 01 2013
|
|
|
REFERENCES
|
R. A. Mollin, Quadratics, CRC Press, 1996, Tables B1-B3.
|
|
|
LINKS
|
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
|
|
|
MATHEMATICA
|
fQ[n_] := Max[Last /@ FactorInteger@ n] == 1 && Mod[n, 4] == 1; Select[ Range@ 272, fQ] (* Robert G. Wilson v *)
Select[Range[300], SquareFreeQ[#]&&Mod[#, 4]==1&] (* Harvey P. Dale, May 24 2012 *)
|
|
|
PROG
|
(MAGMA) [4*n+1: n in [0..67] | IsSquarefree(4*n+1)]; // Bruno Berselli, Mar 03 2011
(Haskell)
a039955 n = a039955_list !! (n-1)
a039955_list = filter ((== 1) . (`mod` 4)) a005117_list
-- Reinhard Zumkeller, Aug 15 2011
|
|
|
CROSSREFS
|
Cf. A002144, A039956, A039957.
Sequence in context: A226165 A166409 A077425 * A213340 A014539 A249034
Adjacent sequences: A039952 A039953 A039954 * A039956 A039957 A039958
|
|
|
KEYWORD
|
nonn,easy,nice
|
|
|
AUTHOR
|
R. K. Guy
|
|
|
STATUS
|
approved
|
| |
|
|
