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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).
7
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
1,10
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.
EXAMPLE
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.
PROG
(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));
CROSSREFS
Cf. A000961 (positions of zeros), A006022, A032742, A052126, A322382, A332993, A332994, A333783, A333784.
Sequence in context: A291971 A240923 A272727 * A323135 A356205 A100258
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 05 2020
STATUS
approved