A051119 n/p^k, where p = largest prime dividing n and p^k = highest power of p dividing n.

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 3, 1, 1, 2, 1, 4, 3, 2, 1, 8, 1, 2, 1, 4, 1, 6, 1, 1, 3, 2, 5, 4, 1, 2, 3, 8, 1, 6, 1, 4, 9, 2, 1, 16, 1, 2, 3, 4, 1, 2, 5, 8, 3, 2, 1, 12, 1, 2, 9, 1, 5, 6, 1, 4, 3, 10, 1, 8, 1, 2, 3, 4, 7, 6, 1, 16, 1, 2, 1, 12, 5, 2, 3, 8, 1, 18, 7, 4, 3, 2, 5, 32, 1, 2, 9, 4, 1

Offset

1,6

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Formula

a(n) = n/A053585(n).

Example

a(36) = 4 because 36/3^2 = 4, 3^2 is highest power dividing 36 of largest prime dividing 36.
a(50) = 50 / 5^2 = 2.

Mathematica

f[n_]:=Module[{c=Last[FactorInteger[n]]}, n/First[c]^Last[c]]; Array[ f, 110] (* Harvey P. Dale, Oct 14 2011 *)

Prog

(Python)
from sympy import factorint, primefactors
def a053585(n):
    if n==1: return 1
    p = primefactors(n)[-1]
    return p**factorint(n)[p]
def a(n): return n/a053585(n) # Indranil Ghosh, May 19 2017

Crossrefs

Cf. A053585(n).

Sequence in context: A074389 A353688 A353666 * A159269 A186728 A158298

Adjacent sequences: A051116 A051117 A051118 * A051120 A051121 A051122

Keyword

nonn,easy,nice

Author

Leroy Quet

Extensions

More terms from James A. Sellers, Jan 21 2000

Status

approved