A333791 - OEIS

%I #15 Apr 05 2020 18:50:20

%S 0,0,0,0,0,1,0,0,0,3,0,3,0,5,2,0,0,4,0,9,4,9,0,7,0,11,0,15,0,12,0,0,8,

%T 15,2,12,0,17,10,21,0,20,0,27,8,21,0,15,0,18,14,33,0,13,6,35,16,27,0,

%U 32,0,29,16,0,8,36,0,45,20,30,0,28,0,35,12,51,4,44,0,45,0,39,0,52,12,41,26,63,0,39,6,63,28,45,14,31

%N Difference of sums of two subsets of divisors of n, those obtained by repeatedly dividing with the smallest remaining prime factor (A332993) and those obtained by repeatedly dividing with the largest remaining prime factor (A332994).

%H Antti Karttunen, <a href="/A333791/b333791.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A333791/a333791.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%F a(n) = A332993(n) - A332994(n).

%F a(n) = A333784(n) - A333783(n).

%F a(n) = A006022(n) - A322382(n).

%F a(p^k) = 0, for all primes p and exponents k >= 0.

%e For n = 12 = 2*2*3, we obtain the A332993(12) = 22 as 12 + 12/2 + 6/2 + 3/3 = 12+6+3+1, and A332994(12) = 19 as 12 + 12/3 + 4/2 + 2/2 = 12+4+2+1, thus a(12) = 22 - 19 = 3.

%o (PARI)

%o A332993(n) = if(1==n,n,n + A332993(n/vecmin(factor(n)[,1])));

%o A332994(n) = if(1==n,n,n + A332994(n/vecmax(factor(n)[,1])));

%o A333791(n) = (A332993(n)-A332994(n));

%Y Cf. A000961 (positions of zeros), A006022, A032742, A052126, A322382, A332993, A332994, A333783, A333784.

%K nonn

%O 1,10

%A _Antti Karttunen_, Apr 05 2020