login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A097015 Smallest x such that Mod[sigma[x], A002110(n)]=A002110(n)-1. 5
1, 2401, 2614689, 36324729, 36324729, 2411675443849, 2411675443849, 12361036649679601 (list; graph; refs; listen; history; text; internal format)
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^(k-2)) = -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 n-th 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 1 02:43 EST 2021. Contains 341732 sequences. (Running on oeis4.)