

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.


3




OFFSET

0,1


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

Table of n, a(n) for n=0..8.
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, 493504; 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), 3746.


MATHEMATICA

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


PROG

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


CROSSREFS

Cf. A000203, A000396, A005100, A005101, A028982, A033879, A033880, A234285, A234286, A294386, A294393, A294406.
Sequence in context: A176399 A273081 A181552 * A229606 A101023 A195303
Adjacent sequences: A294344 A294345 A294346 * A294348 A294349 A294350


KEYWORD

nonn,more,hard


AUTHOR

Omar E. Pol, Oct 29 2017


STATUS

approved



