A243074 a(1) = 1, a(n) = n/p^(k-1), where p = largest prime dividing n and p^k = highest power of p dividing n.

1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 12, 13, 14, 15, 2, 17, 6, 19, 20, 21, 22, 23, 24, 5, 26, 3, 28, 29, 30, 31, 2, 33, 34, 35, 12, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 7, 10, 51, 52, 53, 6, 55, 56, 57, 58, 59, 60, 61, 62, 63, 2, 65, 66, 67, 68, 69, 70, 71, 24, 73, 74, 15, 76, 77, 78, 79, 80, 3

Offset: 1

Author

Antti Karttunen, May 31 2014

Keywords

• nonn

Comments

After 1, A102750 gives such k that a(k) = k, which are also the positions of the records as for all n, a(n) <= n. After 1, only terms of A102750 occur, each an infinite number of times.

Examples

			For n = 18 = 2*3*3, we discard all instances of the highest prime factor 3 except one, thus a(18) = 2*3 = 6.
For n = 54 = 2*3*3*3, we discard two copies of 3, and thus also the value of a(54) is 2*3 = 6.
For n = 20 = 2*5, the highest prime factor 5 occurs only once, so nothing is cast off, and a(20) = 20.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10001

Crossrefs

Differs from A052410 for the first time at n=18.

Cf. A006530, A051119, A102750, A070003, A243057.

Programs

Scheme

(define (A243074 n) (* (A051119 n) (A006530 n)))

Formula

a(n) = A006530(n) * A051119(n).