A068794 In prime factorization of n replace all primes with the least prime factor of n; a(1)=1.

1, 2, 3, 4, 5, 4, 7, 8, 9, 4, 11, 8, 13, 4, 9, 16, 17, 8, 19, 8, 9, 4, 23, 16, 25, 4, 27, 8, 29, 8, 31, 32, 9, 4, 25, 16, 37, 4, 9, 16, 41, 8, 43, 8, 27, 4, 47, 32, 49, 8, 9, 8, 53, 16, 25, 16, 9, 4, 59, 16, 61, 4, 27, 64, 25, 8, 67, 8, 9, 8, 71, 32

Offset: 1

Author

Reinhard Zumkeller, Mar 05 2002

Keywords

• nonn

Comments

a(n)<=n<=A068795(n);

a(n) = A068795(n) iff n=1 or n=p^k for some prime p, k>0.

a(30)=a(2*3*5)=2*2*2=8.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Mathematica

lpf[n_]:=Module[{fi=FactorInteger[n]},Times@@PadRight[{},Total[ fi[[All,2]]], fi[[1,1]]]]; Array[lpf,80] (* Harvey P. Dale, Apr 14 2020 *)

Formula

a(n) = A020639(n)^A001222(n).