A333791 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).

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, 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, 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

Offset: 1

Author

Antti Karttunen, Apr 05 2020

Keywords

• nonn

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

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

Programs

PARI

A332993(n) = if(1==n,n,n + A332993(n/vecmin(factor(n)[,1])));
A332994(n) = if(1==n,n,n + A332994(n/vecmax(factor(n)[,1])));
A333791(n) = (A332993(n)-A332994(n));

Formula

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

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

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

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