login
Integer part of n/(lpf(n)*gpf(n)), where lpf = A020639 is the least prime factor and gpf = A006530 the greatest prime factor.
1

%I #16 Jan 13 2023 10:15:17

%S 1,0,0,1,0,1,0,2,1,1,0,2,0,1,1,4,0,3,0,2,1,1,0,4,1,1,3,2,0,3,0,8,1,1,

%T 1,6,0,1,1,4,0,3,0,2,3,1,0,8,1,5,1,2,0,9,1,4,1,1,0,6,0,1,3,16,1,3,0,2,

%U 1,5,0,12,0,1,5,2,1,3,0,8,9,1,0,6,1,1,1,4,0

%N Integer part of n/(lpf(n)*gpf(n)), where lpf = A020639 is the least prime factor and gpf = A006530 the greatest prime factor.

%C m/(lpf(m)*gpf(m)) is an integer if and only if m is not prime;

%C a(m) = 0 iff m is prime (A000040);

%C for m > 1: a(m) = 1 iff m is semiprime (A001358).

%H Antti Karttunen, <a href="/A070821/b070821.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = floor(A032742(n)/A006530(n)) = floor(A052126(n)/A020639(n)).

%t a[n_] := With[{f = FactorInteger[n]},

%t Floor[n/(f[[1, 1]]*f[[-1, 1]])]];

%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Jan 13 2023 *)

%o (Scheme) (define (A070821 n) (floor->exact (/ (A032742 n) (A006530 n)))) ;; See under A006530, A020639 and A032742 for further code. - _Antti Karttunen_, Aug 12 2017

%Y Cf. A006530, A020639, A032742, A052126.

%K nonn

%O 1,8

%A _Reinhard Zumkeller_, May 15 2002