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%I #14 Dec 01 2019 07:15:51
%S 0,0,0,0,7,47,193,236,1579,4195,18461,62143,275781,1131909,7434169,
%T 10522660,72469339,268486155,1442237845,4284330539,18146555293,
%U 62021099893,248289236937,798007352239,2832660377605,11922780595861
%N Sum of proper divisors minus the number of proper divisors of Catalan number A000108(n).
%H Amiram Eldar, <a href="/A152988/b152988.txt">Table of n, a(n) for n = 0..1667</a>
%F a(n) = A001065(A000108(n)) - A032741(A000108(n)) = A152770(A000108(n)).
%e a(5)=47 because A000108(5)=42 has 7 proper divisors: 1,2,3,6,7,14,21 and 1+2+3+6+7+14+21-7 = 47. - _Emeric Deutsch_, Dec 31 2008
%p with(numtheory): seq(sigma(binomial(2*n, n)/(n+1))-binomial(2*n, n)/(n+1)-tau(binomial(2*n, n)/(n+1))+1, n = 1 .. 27); # _Emeric Deutsch_, Dec 31 2008
%t diff[n_] := DivisorSigma[1, n] - DivisorSigma[0, n] - n + 1; Table[diff[ CatalanNumber[n] ], {n, 0, 25}] (* _Amiram Eldar_, Dec 01 2019 *)
%Y Cf. A000005, A000108, A000203, A001065, A032741, A152770.
%K nonn
%O 0,5
%A _Omar E. Pol_, Dec 20 2008, Jan 07 2009
%E Extended by _Emeric Deutsch_, Dec 31 2008