A378600 - OEIS

%I #9 Dec 04 2024 20:54:16

%S 1,1,2,1,4,0,6,1,5,2,10,0,12,4,6,1,16,-1,18,0,10,8,22,0,19,10,14,0,28,

%T 0,30,1,18,14,22,-1,36,16,22,0,40,0,42,4,12,20,46,0,41,7,30,6,52,0,38,

%U 0,34,26,58,0,60,28,22,1,46,0,66,10,42,0,70,-1,72,34,26,12,58,0,78,0,41,38,82,0,62,40,54,0,88,0,70

%N Signed variant of Zumkeller deficiency: a(n) = signum(A033879(n)) * A103977(n).

%C If n is abundant, then negate the value of A103977(n), otherwise use as it is.

%H Antti Karttunen, <a href="/A378600/b378600.txt">Table of n, a(n) for n = 1..20000</a>

%F If A033879(n) >= 0, a(n) = A033879(n), otherwise a(n) = -A103977(n).

%o (PARI)

%o A033879(n) = (n+n-sigma(n));

%o nonzerocoefpositions(p) = { my(v=Vec(p), lista=List([])); for(i=1,#v,if(v[i], listput(lista,i))); Vec(lista); };

%o A103977(n) = { my(p=1); fordiv(n, d, p *= (1 + 'x^d)); my(plist=nonzerocoefpositions(p), m = #plist, d); if(!(m%2), plist[1+(m/2)]-plist[m/2], d = plist[(m+1)/2]-plist[(m-1)/2]; if(1==d,0,d)); };

%o A378600(n) = { my(d=A033879(n)); if(d>=0, d, -A103977(n)); };

%Y Cf. A033879, A103977.

%Y Cf. A005100 (positions of terms > 0), A083207 (positions of 0's), A083211 (positions of negative terms), A156903 (positions of odd negative terms), A171641 (of even negative terms).

%K sign,new

%O 1,3

%A _Antti Karttunen_, Dec 04 2024