cp's OEIS Frontend

A294347 a(n) is the smallest number whose deficiency or abundance is equal to n, or a(n) = 0 if such a number does not exist.

%I A294347 #60 Nov 01 2017 16:09:27
%S A294347 6,1,3,18,5,9,7,50,22
%N A294347 a(n) is the smallest number whose deficiency or abundance is equal to n, or a(n) = 0 if such a number does not exist.
%C A294347 If nonzero, a(9) > 10^9. - _Michel Marcus_, Oct 29 2017
%C A294347 From _Robert Israel_, Oct 29 2017: (Start)
%C A294347 If n is odd, then a(n) must be a square or twice a square (A028982).
%C A294347 If nonzero, a(9) > 10^13.
%C A294347 Some other values: a(11)=244036, a(17)=100, a(19)=25, a(25)=98, a(31)=15376, a(37)=484, a(39)=162, a(41)=49, a(47)=225, a(51)=72. (End)
%C A294347 a(n) > 10^20 for n in (9, 13, 15, 21, 23, 27, 29, 33, 35, 43, 45); see the intersection of A234285 and A234286. - _Michel Marcus_, Oct 30 2017
%C A294347 For the intersection mentioned above see A294406. - _Omar E. Pol_, Nov 01 2017
%H A294347 Nichole Davis, Dominic Klyve and Nicole Kraght, <a href="http://dx.doi.org/10.2140/involve.2013.6.493">On the difference between an integer and the sum of its proper divisors</a>, Involve, Vol. 6 (2013), No. 4, 493-504; DOI: 10.2140/involve.2013.6.493.
%H A294347 Raven Dean, Rick Erdman, Dominic Klyve, Emily Lycette, Melissa Pidde, and Derek Wheel, <a href="https://projecteuclid.org/euclid.mjms/1449161366">Families of Values of the Excedent Function sigma(n)-2n</a>, Missouri J. Math. Sci., Volume 27, Issue 1 (2015), 37-46.
%t A294347 Table[k = 1; While[Abs[2 k - DivisorSigma[1, k]] != n, k++]; k, {n, 0, 8}] (* _Michael De Vlieger_, Oct 30 2017 *)
%o A294347 (PARI) a(n) = {my(k=1); while (abs(2*k-sigma(k)) != n, k++); k;} \\ _Michel Marcus_, Oct 29 2017
%Y A294347 Cf. A000203, A000396, A005100, A005101, A028982, A033879, A033880, A234285, A234286, A294386, A294393, A294406.
%K A294347 nonn,more,hard
%O A294347 0,1
%A A294347 _Omar E. Pol_, Oct 29 2017