login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A025473 a(1) = 1; for n > 1, a(n) = prime root of n-th prime power (A000961). 29
1, 2, 3, 2, 5, 7, 2, 3, 11, 13, 2, 17, 19, 23, 5, 3, 29, 31, 2, 37, 41, 43, 47, 7, 53, 59, 61, 2, 67, 71, 73, 79, 3, 83, 89, 97, 101, 103, 107, 109, 113, 11, 5, 127, 2, 131, 137, 139, 149, 151, 157, 163, 167, 13, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
This sequence is related to the cyclotomic sequences A013595 and A020500, leading to the procedure used in the Mathematica program. - Roger L. Bagula, Jul 08 2008
From Reinhard Zumkeller, Jun 26 2011: (Start)
A000961(n) = a(n)^A025474(n); A056798(n) = a(n)^(2*A025474(n));
A192015(n) = A025474(n)*a(n)^(A025474(n)-1). (End)
"LCM numeral system": a(n+1) is radix for index n, n >= 0; a(-n+1) is 1/radix for index n, n < 0. - Daniel Forgues, May 03 2014
This is the LCM-transform of A000961; same as A014963 with all 1's (except a(1)) removed. - David James Sycamore, Jan 11 2024
REFERENCES
Paul J. McCarthy, Algebraic Extensions of Fields, Dover books, 1976, pages 40, 69
LINKS
Eric Weisstein's World of Mathematics, Cyclotomic Polynomial
FORMULA
a(n) = A006530(A000961(n)) = A020639(A000961(n)). - David Wasserman, Feb 16 2006
MAPLE
cvm := proc(n, level) local f, opf; if n < 2 then RETURN() fi;
f := ifactors(n); opf := op(1, op(2, f)); if nops(op(2, f)) > 1 or
op(2, opf) <= level then RETURN() fi; op(1, opf) end:
A025473_list := n -> [1, seq(cvm(i, 0), i=1..n)];
A025473_list(240); # Peter Luschny, Sep 21 2011
MATHEMATICA
a = Join[{1}, Flatten[Table[If[PrimeQ[Apply[Plus, CoefficientList[Cyclotomic[n, x], x]]], Apply[Plus, CoefficientList[Cyclotomic[n, x], x]], {}], {n, 1, 1000}]]] (* Roger L. Bagula, Jul 08 2008 *)
Join[{1}, First@ First@# & /@ FactorInteger@ Select[Range@ 240, PrimePowerQ]] (* Robert G. Wilson v, Aug 17 2017 *)
PROG
(Sage)
def A025473_list(n) :
R = [1]
for i in (2..n) :
if i.is_prime_power() :
R.append(prime_divisors(i)[0])
return R
A025473_list(239) # Peter Luschny, Feb 07 2012
(Haskell)
a025473 = a020639 . a000961 -- Reinhard Zumkeller, Aug 14 2013
(PARI) print1(1); for(n=2, 1e3, if(isprimepower(n, &p), print1(", "p))) \\ Charles R Greathouse IV, Apr 28 2014
CROSSREFS
Sequence in context: A286151 A192138 A175264 * A351847 A192141 A092556
KEYWORD
easy,nonn,nice
AUTHOR
David W. Wilson, Dec 11 1999
EXTENSIONS
Offset corrected by David Wasserman, Dec 22 2008
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)