A054904 - OEIS

%I #15 Mar 24 2020 14:03:54

%S 104,65,20,80,44,125,45,63,40,99,56,70,296,125,88,110,104,145,212,182,

%T 80,170,333,105,369,185,184,135,180,301,356,185,1859,329,176,195,4916,

%U 434,612,287,140,185,776,255,524,413,344,205,272,329,567,215,320,469

%N x = a(n) is the smallest composite number such that sigma(x+6n) = sigma(x)+6n, where sigma = A000203.

%C If sigma(x+d) = sigma(x)+d and d = 6k, then composite solutions seem to be more frequent and arise sooner.

%C a(725) > 3*10^11 (if it exists). - _Donovan Johnson_, Sep 23 2013

%H Donovan Johnson, <a href="/A054904/b054904.txt">Table of n, a(n) for n = 1..724</a>

%F sigma(x+6n) = sigma(x)+6n, a(n) = min(x) and it is composite.

%e n = 20, 6n = 120, a(20) = 182, sigma(182)+120 = 336+120 = 456 = sigma(182+120) = sigma(302).

%t 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 *)

%o (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 */

%Y Cf. A015914-A015917, A023200-A023203, A054799, A054903-A054905.

%K nonn

%O 1,1

%A _Labos Elemer_, May 23 2000