A333791 - OEIS

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

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OFFSET

1,10

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

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

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

Adjacent sequences: A333788 A333789 A333790 * A333792 A333793 A333794

KEYWORD

nonn

AUTHOR

Antti Karttunen, Apr 05 2020

STATUS

approved