A075491 - OEIS

A075491

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

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, -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, 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

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OFFSET

1,5

LINKS

Table of n, a(n) for n=1..110.

FORMULA

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

EXAMPLE

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

MATHEMATICA

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

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