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

1,2

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.

Links

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

Formula

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

Example

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.

Prog

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

Crossrefs

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

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

Sequence in context: A166140 A019555 A378997 * A304776 A052410 A327501

Adjacent sequences: A243071 A243072 A243073 * A243075 A243076 A243077

Keyword

nonn

Author

Antti Karttunen, May 31 2014

Status

approved