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

1,2

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

Links

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

Example

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.

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 *)

Prog

(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
(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

Crossrefs

Cf. A007947.

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

Cf. A027748, A124010, A051903.

Sequence in context: A162323 A165743 A086297 * A281495 A056554 A346486

Adjacent sequences: A261966 A261967 A261968 * A261970 A261971 A261972

Keyword

nonn

Author

Franklin T. Adams-Watters, Sep 07 2015

Status

approved