

A097015


Smallest x such that Mod[sigma[x], A002110(n)]=A002110(n)1.


5




OFFSET

1,2


COMMENTS

10^19 < a(9) <= 725298909352131113041. Terms a(3) through a(8) all have the prime signature p^4*q^2*r^2. Any x such that sigma(x) = 1 (mod 30) must have at least eight prime factors. However, for all n, there are solutions with fewer than three distinct prime factors. More generally, for any k > 1, let p be a prime of the form mk+1; then sigma(p^(k2)) = 1 (mod k). For a(9), 725298909352131113041 is the least solution with eight prime factors. I have not been able to rule out a smaller solution with more prime factors.  David Wasserman, Dec 14 2007


LINKS

Table of n, a(n) for n=1..8.


EXAMPLE

Smallest numbers x are collected, whose sigma[x] has 2k+1,6k+5,30k+29,210k+209 etc.. form; i.e. for which 1+sigma[x] is divisible by the nth primorial number


CROSSREFS

Cf. A084301, A084303, A000203, A097011, A097012, A097014, A097015.
Sequence in context: A017608 A061210 A226092 * A222461 A013845 A031776
Adjacent sequences: A097012 A097013 A097014 * A097016 A097017 A097018


KEYWORD

nonn


AUTHOR

Labos Elemer, Aug 19 2004


EXTENSIONS

More terms from David Wasserman, Dec 14 2007


STATUS

approved



