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.

6, 1, 3, 18, 5, 9, 7, 50, 22

Offset: 0

Author

Omar E. Pol, Oct 29 2017

Keywords

• nonn
• more
• hard

Comments

If nonzero, a(9) > 10^9. - Michel Marcus, Oct 29 2017

From Robert Israel, Oct 29 2017: (Start)

If n is odd, then a(n) must be a square or twice a square (A028982).

If nonzero, a(9) > 10^13.

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)

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

For the intersection mentioned above see A294406. - Omar E. Pol, Nov 01 2017

Links

• Nichole Davis, Dominic Klyve and Nicole Kraght, On the difference between an integer and the sum of its proper divisors, Involve, Vol. 6 (2013), No. 4, 493-504; DOI: 10.2140/involve.2013.6.493.
• Raven Dean, Rick Erdman, Dominic Klyve, Emily Lycette, Melissa Pidde, and Derek Wheel, Families of Values of the Excedent Function sigma(n)-2n, Missouri J. Math. Sci., Volume 27, Issue 1 (2015), 37-46.

Crossrefs

Cf. A000203, A000396, A005100, A005101, A028982, A033879, A033880, A234285, A234286, A294386, A294393, A294406.

Programs

Mathematica

Table[k = 1; While[Abs[2 k - DivisorSigma[1, k]] != n, k++]; k, {n, 0, 8}] (* Michael De Vlieger, Oct 30 2017 *)

PARI

a(n) = {my(k=1); while (abs(2*k-sigma(k)) != n, k++); k;} \\ Michel Marcus, Oct 29 2017