|
Search: id:A007947
|
|
|
| A007947 |
|
Largest square-free number dividing n (the square-free kernel of n). |
|
+0
225
|
|
| 1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 6, 13, 14, 15, 2, 17, 6, 19, 10, 21, 22, 23, 6, 5, 26, 3, 14, 29, 30, 31, 2, 33, 34, 35, 6, 37, 38, 39, 10, 41, 42, 43, 22, 15, 46, 47, 6, 7, 10, 51, 26, 53, 6, 55, 14, 57, 58, 59, 30, 61, 62, 21, 2, 65, 66, 67, 34, 69, 70, 71, 6, 73, 74, 15, 38, 77, 78
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Sometimes called rad(n).
Multiplicative with a(p^n) = p.
For n>1, product of the distinct prime factors of n.
a(k)=k for k=square-free numbers A005117. - Lekraj Beedassy (blekraj(AT)yahoo.com), Sep 05 2006
A note on square roots of numbers: we can write sqrt(n) = b*sqrt(c) where c is squarefree. Then b = A000188(n) is the "inner square root" of n, c = A007913(n), LCM(b,c) = A007947(n) = "squarefree kernel" of n and bc = A019554(n) = "outer square root" of n.
a(n) = A128651(A129132(n-1) + 2) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 30 2007
|
|
REFERENCES
|
J. Grytczuk, Thue type problems for graphs, points and numbers, Discrete Math., 308 (2008), 4419-4429.
S. Lang, Old and New Conjectured Diophantine Inequalities, Bull. Amer. Math. Soc., 23 (1990), 37-75. see p. 39.
F. Smarandache, "Only Problems, not Solutions!", Xiquan Publ., Phoenix-Chicago, 1993
|
|
LINKS
|
Daniel Forgues, Table of n, a(n) for n=1..100000
H. Bottomley, Some Smarandache-type multiplicative sequences
S. R. Finch, Unitarism and infinitarism.
Neville Holmes, Integer Sequences
M. L. Perez et al., eds., Smarandache Notions Journal
I. Peterson, The Amazing ABC Conjecture
F. Smarandache, Only Problems, Not Solutions!.
|
|
FORMULA
|
n = Product (p_j^k_j) -> Product (p_j).
Multiplicative with a(p^k) = p. - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001.
|
|
MAPLE
|
with(numtheory); A007947 := proc(n) local i, t1, t2; t1 := ifactors(n)[2]; t2 := mul(t1[i][1], i=1..nops(t1)); end;
|
|
MATHEMATICA
|
Prepend[ Array[ Times @@ First[ Transpose[ FactorInteger[ # ] ] ]&, 100, 2 ], 1 ]
|
|
PROGRAM
|
(PARI) a(n)=local(p); p=factor(n)[, 1]; prod(i=1, length(p), p[i])
(MAGMA) [ &*PrimeDivisors(n): n in [1..100] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 04 2008]
|
|
CROSSREFS
|
Cf. A048803, A007913, A062953.
Cf. A000188 A007913 A019554
Sequence in context: A086297 A056554 A088835 this_sequence A015053 A062953 A015052
Adjacent sequences: A007944 A007945 A007946 this_sequence A007948 A007949 A007950
|
|
KEYWORD
|
nonn,easy,nice,mult
|
|
AUTHOR
|
R. Muller
|
|
EXTENSIONS
|
More terms from several people including David W. Wilson (davidwwilson(AT)comcast.net).
|
|
|
Search completed in 0.004 seconds
|
