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A025473
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a(1) = 1; for n > 1, a(n) = prime root of n-th prime power (A000961).
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28
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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
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OFFSET
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1,2
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COMMENTS
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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
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REFERENCES
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Paul J. McCarthy, Algebraic Extensions of Fields, Dover books, 1976, pages 40, 69
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LINKS
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David Wasserman, Table of n, a(n) for n = 1..1000
OEIS Wiki, LCM numeral system
Eric Weisstein's World of Mathematics, Cyclotomic Polynomial
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FORMULA
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a(n) = A006530(A000961(n)) = A020639(A000961(n)). - David Wasserman, Feb 16 2006
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A013595, A020500, A025476.
Sequence in context: A286151 A192138 A175264 * A192141 A092556 A092550
Adjacent sequences: A025470 A025471 A025472 * A025474 A025475 A025476
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KEYWORD
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easy,nonn,nice
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AUTHOR
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David W. Wilson, Dec 11 1999
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EXTENSIONS
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Offset corrected by David Wasserman, Dec 22 2008
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STATUS
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approved
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