

A243074


a(1) = 1, a(n) = n/p^(k1), where p = largest prime dividing n and p^k = highest power of p dividing n.


2



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
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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: A053166 A166140 A019555 * A304776 A052410 A327501
Adjacent sequences: A243071 A243072 A243073 * A243075 A243076 A243077


KEYWORD

nonn


AUTHOR

Antti Karttunen, May 31 2014


STATUS

approved



