|
%I #16 Dec 18 2017 11:57:02
%S 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,
%T 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,
%U 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
%N The truncated kernel function of n: the product of distinct primes dividing n, but excluding the largest prime divisor of n.
%C 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)).
%H Antti Karttunen, <a href="/A293810/b293810.txt">Table of n, a(n) for n = 1..16384</a>
%H J.-M. De Koninck, I. Diouf, N. Doyon, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL15/DeKoninck/dek12.html">On the truncated kernel function</a>, J. Int. Seq. 15 (2012) #12.3.2.
%F a(n) = A007947(n)/A006530(n).
%p A293810 := proc(n)
%p if n =1 then
%p 1;
%p else
%p A007947(n)/A006530(n) ;
%p end if;
%p end proc:
%p seq(A293810(n),n=1..120) ;
%t Array[Times @@ Most@ FactorInteger[#][[All, 1]] &, 105] (* _Michael De Vlieger_, Dec 16 2017 *)
%o (Scheme) (define (A293810 n) (/ (A007947 n) (A006530 n))) ;; _Antti Karttunen_, Dec 16 2017
%Y Cf. A007947, A006530.
%K nonn
%O 1,6
%A _R. J. Mathar_, Oct 16 2017
%E Amended the name with the explanation from the Comments section; also more terms added by _Antti Karttunen_, Dec 16 2017
|
