%I #9 Aug 20 2019 02:16:33
%S 0,1,2,4,3,7,4,9,8,9,4,17,6,10,14,18,5,20,6,21,16,12,4,33,14,13,18,24,
%T 6,33,8,29,18,12,18,44,9,13,17,41,8,37,8,26,39,14,4,57,18,30,20,28,6,
%U 41,20,45,20,14,4,68,12,16,40,46,25,43,8,25,18,44,8,80,12,16,42,30,22,42,8
%N Sum_{d<n is a divisor of n} tau(n-d).
%F It appears that a(n) > tau(n) for n >= 4.
%e a(9) = tau(9-1)+tau(9-3) = tau(8)+tau(6) = 4+4 = 8.
%p with(numtheory): a:=proc(n) local div: div:=divisors(n): sum(tau(n-div[j]),j=1..tau(n)-1): end: seq(a(n),n=2..90); # _Emeric Deutsch_, Aug 05 2005
%t f[n_] := Plus @@ (DivisorSigma[0, n - # ] & /@ Most[Divisors[n]]); Table[ f[n], {n, 79}] (* _Robert G. Wilson v_, Aug 05 2005 *)
%o (PARI) a(n) = sumdiv(n, d, if (d<n, numdiv(n-d))); \\ _Michel Marcus_, Aug 20 2019
%Y Cf. A007425.
%K nonn
%O 1,3
%A _Amarnath Murthy_, Jul 31 2005
%E Edited, corrected and extended by _Emeric Deutsch_ and _Robert G. Wilson v_, Aug 05 2005