A261969 Product of primes dividing n with maximum multiplicity.

1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 2, 13, 14, 15, 2, 17, 3, 19, 2, 21, 22, 23, 2, 5, 26, 3, 2, 29, 30, 31, 2, 33, 34, 35, 6, 37, 38, 39, 2, 41, 42, 43, 2, 3, 46, 47, 2, 7, 5, 51, 2, 53, 3, 55, 2, 57, 58, 59, 2, 61, 62, 3, 2, 65, 66, 67, 2, 69, 70, 71, 2, 73, 74, 5, 2, 77, 78, 79, 2, 3, 82, 83, 2, 85, 86, 87, 2, 89, 3, 91

Offset: 1

Author

Franklin T. Adams-Watters, Sep 07 2015

Keywords

• nonn

Comments

a(1) = 1 by convention.

If n is prime then a(n) = n; e.g., a(2) = 2, a(3) = 3, a(5) = 5, etc. Also if n is nonsquare semiprime then a(n) = n; e.g., a(6) = 6, a(10) = 10, a(14) = 14, a(15) = 15, etc. - Zak Seidov, Sep 07 2015

a(n)= n precisely when n is squarefree. - Franklin T. Adams-Watters, Feb 16 2019

Examples

			18 = 2^1 * 3^2. 2 is the maximum exponent, 3 is the only prime with that exponent, so a(18) = 3.
36 = 2^2 * 3^2, maximum exponent 2 for both 2 and 3, so a(36) = 2*3 = 6.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007947.

Cf. A000040, A001358. - Zak Seidov, Sep 07 2015

Cf. A027748, A124010, A051903.

Programs

Haskell

a261969 n = product $ map fst $ filter ((== emax) . snd) $ zip ps es
    where emax = maximum es
          ps = a027748_row n; es = a124010_row n
-- Reinhard Zumkeller, Sep 08 2015

Maple

a:= n-> (l->(m->mul(`if`(m=j[2], j[1], 1), j=l))(
         max(seq(i[2], i=l))))(ifactors(n)[2]):
seq(a(n), n=1..100);  # Alois P. Heinz, Sep 07 2015

Mathematica

f[n_] := Block[{pf = FactorInteger@ n}, Times @@ Take[First /@ pf, Flatten@ Position[Last /@ pf, Max[Last /@ pf]]]]; f /@ Range@ 91 (* Michael De Vlieger, Sep 07 2015 *)

PARI

a(n) = my(fm=factor(n),m); if(n<2,return(n)); m=vecmax(fm[,2]~); prod(k=1,#fm[,2]~,if(fm[k,2]==m,fm[k,1],1))

PARI

a(n) = {my(f = factor(n)); if (n>1, m = vecmax(f[,2])); for (i=1, #f~, f[i,2] = (f[i,2]==m)); factorback(f);} \\ Michel Marcus, Sep 08 2015