cp's OEIS Frontend

A218767 Total number of divisors and anti-divisors of n.

%I A218767 #22 Feb 18 2013 03:08:38
%S A218767 1,2,3,4,4,5,5,6,5,7,5,8,6,7,7,7,7,10,5,9,7,9,7,10,8,7,9,11,5,11,7,12,
%T A218767 9,7,9,11,7,11,9,12,6,13,7,9,13,9,7,13,9,12,7,13,9,11,9,11,9,11,9,18,
%U A218767 6,9,13,9,9,13,11,13,7,13,7,18,9,9,11,11,13,13,5,15,11,11,9,16,12,9
%N A218767 Total number of divisors and anti-divisors of n.
%C A218767 Or tau(n) + anti-tau(n), where anti-tau = A066272.
%C A218767 Total sum of divisors and anti-divisors of n or sigma(n) + A066417(n): 1, 3, 6, 10, 11, 16, 18, 23, 21, 32, 24, 41, 33, 40, 42, 45, 46, 67, 38, 66, 54, 72, 58, 83, 70, 66, 82, 102, 54, 108,...
%C A218767 Numbers n such that sigma(n) = n + anti-sigma(n): A074751.
%C A218767 Numbers n such that Chowla's function(n) = anti-sigma(n): 1, 2, 16, 60, 72,...
%C A218767 Number of divisors of n minus number of anti-divisors of n or tau(n) - anti-tau(n): 1, 2, 1, 2, 0, 3, -1, 2, 1, 1, -1, 4, -2, 1, 1, 3, -3, 2, -1, 3, 1, -1, -3, 6, -2, 1, -1, 1, -1, 5, -3, 0, -1, 1, -1, 7, -3, -3, -1, 4, -2, 3, -3, 3, -1,...
%C A218767 Product of number of divisors of n and number of anti-divisors of n, or tau(n)*anti-tau(n): 0, 0, 2, 3, 4, 4, 6, 8, 6, 12, 6, 12, 8, 12, 12, 10, 10, 24, 6, 18, 12, 20, 10, 16, 15, 12, 20, 30, 6, 24,...
%C A218767 Number of ways to write n as k*(k - m) with k divisor and m anti-divisor of n: 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0,...
%C A218767 Numbers which are not of the form k*(k - m), k divisor, m anti-divisor (i.e., where the number of ways is zero): 1, 2, 5, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 19, 21, 23, 24, 25, 26, 29,
%F A218767 a(n) = A000005(n) + A066272(n).
%p A218767 A218767 := proc(n)
%p A218767         numtheory[tau](n)+A066272(n) ;
%p A218767 end proc: # _R. J. Mathar_, Feb 16 2013
%Y A218767 Cf. A000005, A000203, A001065, A066272, A066417, A027750, A048050, A130799.
%K A218767 nonn
%O A218767 1,2
%A A218767 _Juri-Stepan Gerasimov_, Feb 05 2013