OFFSET
1,1
COMMENTS
If sigma(x+d) = sigma(x)+d and d = 6k, then composite solutions seem to be more frequent and arise sooner.
a(725) > 3*10^11 (if it exists). - Donovan Johnson, Sep 23 2013
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..724
FORMULA
sigma(x+6n) = sigma(x)+6n, a(n) = min(x) and it is composite.
EXAMPLE
n = 20, 6n = 120, a(20) = 182, sigma(182)+120 = 336+120 = 456 = sigma(182+120) = sigma(302).
MATHEMATICA
Table[x = 4; While[Nand[CompositeQ@ x, DivisorSigma[1, x + 6 n] == DivisorSigma[1, x] + 6 n], x++]; x, {n, 54}] (* Michael De Vlieger, Feb 18 2017 *)
PROG
(PARI) /* finds first 696 terms */ mx=7695851; s=vector(mx); for(j=4, mx, if(isprime(j)==0, s[j]=sigma(j))); for(n=1, 696, n6=n*6; for(x=4, 7691753, if(s[x]>0, if(s[x+n6]==s[x]+n6, write("b054904.txt", n " " x); next(2))))) /* Donovan Johnson, Sep 23 2013 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, May 23 2000
STATUS
approved