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A025473 a(1) = 1; for n > 1, a(n) = prime root of n-th prime power (A000961). 28
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

REFERENCES

Paul J. McCarthy, Algebraic Extensions of Fields, Dover books, 1976, pages 40, 69

LINKS

David Wasserman, Table of n, a(n) for n = 1..1000

OEIS Wiki, LCM numeral system

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

Cf. A013595, A020500, A025476.

Sequence in context: A286151 A192138 A175264 * A192141 A092556 A092550

Adjacent sequences:  A025470 A025471 A025472 * A025474 A025475 A025476

KEYWORD

easy,nonn,nice

AUTHOR

David W. Wilson, Dec 11 1999

EXTENSIONS

Offset corrected by David Wasserman, Dec 22 2008

STATUS

approved

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Last modified July 21 06:55 EDT 2019. Contains 325192 sequences. (Running on oeis4.)