A293810 - OEIS

A293810

The truncated kernel function of n: the product of distinct primes dividing n, but excluding the largest prime divisor of n.

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 1, 6, 1, 1, 3, 2, 5, 2, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 5, 2, 3, 2, 1, 6, 1, 2, 3, 1, 5, 6, 1, 2, 3, 10, 1, 2, 1, 2, 3, 2, 7, 6, 1, 2, 1, 2, 1, 6, 5, 2, 3, 2, 1, 6, 7, 2, 3, 2, 5, 2, 1, 2, 3, 2, 1, 6, 1, 2, 15

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OFFSET

1,6

COMMENTS

Contains the product of the distinct primes dividing n (like the kernel function A007947) but excluding the largest prime dividing n (which is A006530(n)).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

J.-M. De Koninck, I. Diouf, N. Doyon, On the truncated kernel function, J. Int. Seq. 15 (2012) #12.3.2.

FORMULA

a(n) = A007947(n)/A006530(n).

MAPLE

A293810 := proc(n)

if n =1 then

else

A007947(n)/A006530(n) ;

end if;

end proc:

seq(A293810(n), n=1..120) ;

MATHEMATICA

Array[Times @@ Most@ FactorInteger[#][[All, 1]] &, 105] (* Michael De Vlieger, Dec 16 2017 *)

PROG

(Scheme) (define (A293810 n) (/ (A007947 n) (A006530 n))) ;; Antti Karttunen, Dec 16 2017

CROSSREFS

Cf. A007947, A006530.

Sequence in context: A187279 A076820 A206824 * A356553 A324369 A276781

Adjacent sequences: A293807 A293808 A293809 * A293811 A293812 A293813

KEYWORD

nonn

AUTHOR

R. J. Mathar, Oct 16 2017

EXTENSIONS

Amended the name with the explanation from the Comments section; also more terms added by Antti Karttunen, Dec 16 2017

STATUS

approved