A293438 - OEIS

%I #6 Dec 01 2017 18:51:32

%S 1,1,1,1,1,2,1,1,2,4,1,0,1,6,8,1,1,0,1,8,12,10,1,0,4,12,10,24,1,0,1,1,

%T 20,16,24,0,1,18,24,-16,1,0,1,80,240,22,1,0,6,152,32,120,1,0,40,0,36,

%U 28,1,0,1,30,600,1,48,0,1,224,44,4224,1,0,1,36,912,288,60,0,1,160,140,40,1,0,64,42,56,320,1,0,72,440,60,46,72

%N Product of deficiencies of proper divisors of n.

%C There are only 643 negative values in range 1 .. 16384.

%H Antti Karttunen, <a href="/A293438/b293438.txt">Table of n, a(n) for n = 1..16384</a>

%F a(n) = Product_{d|n, d<n} A033879(d).

%F a(A000040(n)) = 1, a(A000079(n)) = 1.

%e The proper divisors of 15 are 1, 3, 5. Their deficiencies (A033879) are 1, 2, 4. Thus a(15) = 1*2*4 = 8.

%e The proper divisors of 18 are 1, 2, 3, 6, 9. Their deficiencies are 1, 1, 2, 0, 5, thus a(18) = 1*1*2*0*5 = 0.

%e The proper divisors of 40 are 1, 2, 4, 5, 8, 10, 20. Their deficiencies are 1, 1, 1, 4, 1, 2, -2, thus a(40) = 1 * 1 * 1 * 4 * 1 * 2 * -2 = -16.

%o (PARI)

%o A033879(n) = ((2*n)-sigma(n));

%o A293438(n) = { my(m=1); fordiv(n,d,if(d<n,m *= A033879(d))); (m); };

%Y Cf. A033879, A286449.

%K sign

%O 1,6

%A _Antti Karttunen_, Dec 01 2017