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A157449 Difference between n and the sum of its divisors except 1 and itself. 4

%I #21 May 03 2023 08:59:03

%S 2,3,2,5,1,7,2,6,3,11,-3,13,5,7,2,17,-2,19,-1,11,9,23,-11,20,11,15,1,

%T 29,-11,31,2,19,15,23,-18,37,17,23,-9,41,-11,43,5,13,21,47,-27,42,8,

%U 31,7,53,-11,39,-7,35,27,59,-47,61,29,23,2

%N Difference between n and the sum of its divisors except 1 and itself.

%C a(n) = n - k where k is the sum of the divisors of n excluding 1 and n itself. The initial value for n is 2.

%C Evidently a(n) = n iff n is prime (A000040). Moreover a(n) = 1 iff n is perfect (A000396).

%C A value of 0 indicates a quasiperfect number, although no such number is known. - _Felix Fröhlich_, Jul 14 2014

%C a(n) is negative iff n is abundant (A005101). - _Christian N. K. Anderson_, May 02 2023

%H Ferruccio Guidi, <a href="/A157449/b157449.txt">Table of n, a(n) for n=2..100001</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Quasiperfect_number">Quasiperfect number</a>

%F a(n) = (2*n+1)-A000203(n). - _Felix Fröhlich_, Jul 14 2014

%e The divisors of 10 are 1, 2, 5 and 10, so a(10) = 10 - (2 + 5) = 3.

%t Table[2n+1-DivisorSigma[1,n],{n,70}] (* _Harvey P. Dale_, Jul 22 2013 *)

%o (PARI) for(n=2, 1e2, a=2*n+1; b=sigma(n); print1(a-b, ", ")) \\ _Felix Fröhlich_, Jul 14 2014

%Y Cf. A000040, A000203, A000396, A005101.

%K sign,easy

%O 2,1

%A Ferruccio Guidi (fguidi(AT)cs.unibo.it), Mar 01 2009

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)