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Sum of digits of n minus number of divisors of n.
2

%I #10 Nov 21 2013 12:47:53

%S 0,0,1,1,3,2,5,4,6,-3,0,-3,2,1,2,2,6,3,8,-4,-1,0,3,-2,4,4,5,4,9,-5,2,

%T -1,2,3,4,0,8,7,8,-4,3,-2,5,2,3,6,9,2,10,-1,2,1,6,1,6,3,8,9,12,-6,5,4,

%U 3,3,7,4,11,8,11,-1,6,-3,8,7,6,7,10,7,14,-2,4,6,9,0,9,10,11,8,15,-3,6,5,8,9,10,3,14,11,12,-8,0,-5,2,-3,-2,3,6,-3,8,-6

%N Sum of digits of n minus number of divisors of n.

%F a(n)=A007953[n]-A000005[n]

%e a[n]<0, see A075492, n=10, 20, 30, ... a[n]=0, see A057531, primes like 2, 11, 101 a[n]>0, see A075493, majority of primes and others

%t sud[x_] := Apply[Plus, IntegerDigits[x]] Table[sud[w]-DivisorSigma[0, w], {w, 1, 128}]

%t f[n_]:=Total[IntegerDigits[n]]-DivisorSigma[0,n];Array[f,130] (* _Harvey P. Dale_, Aug 10 2011 *)

%Y Cf. A007953, A000005, A057531, A075492, A075493.

%K base,easy,sign

%O 1,5

%A _Labos Elemer_, Sep 26 2002