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%I #38 Sep 10 2019 21:18:59
%S 6,57,443,1407,1410,12242,15051,30952,44277,65190,68697,609531,921774,
%T 951092,2012670,2820460,11961680,32886944,3450005970
%N Numbers k such that k | (sigma(k-2) + sigma(k-1) + sigma(k+1) + sigma(k+2)).
%C Values of the ratio ( sigma(k-2)+sigma(k-1)+sigma(k+1)+sigma(k+2) ) / k: 6, 6, 7, 6, 6, 8, 6, 7, 6, 6, 6, 6, 6, 7, 6, 6, ...
%e 6 is in the sequence because (sigma(4) + sigma(5) + sigma(7) + sigma(8))/6 = (7 + 6 + 8 + 15)/6 = 6;
%e 443 is in the sequence because (sigma(441) + sigma(442) + sigma(444) + sigma(445))/443 = (741 + 756 + 1064 + 540)/443 = 7.
%p with(numtheory): P:=proc(q) local a,b,c,d,f,k,n;
%p a:=sigma(0); b:=sigma(1); c:=sigma(2); d:=sigma(3); f:=sigma(4);
%p for n from 2 to q do if type((a+b+d+f)/n,integer) then print(n,(a+b+d+f)/n); fi; a:=b; b:=c; c:=d; d:=f; f:=sigma(n+3); od; end: P(10^9);
%o (PARI) lista(nn) = {my(v = vector(nn, k, sigma(k))); for (k=3, nn-3, if (!((v[k-2]+v[k-1]+v[k+1]+v[k+2]) % k), print1(k, ", ")););} \\ _Michel Marcus_, Sep 10 2019
%o (PARI) upto(n) = my(v=List(vector(5,i,sigma(i))), res=List()); for(i=6, n, if((v[1] + v[2] + v[4] + v[5]) % (i-3) == 0, listput(res, i-3)); listpop(v,1); listput(v,sigma(i))); res \\ _David A. Corneth_, Sep 10 2019
%Y Cf. A186103, A227306.
%K nonn,more
%O 1,1
%A _Paolo P. Lava_, Dec 04 2017
%E Term 2 removed and a(17)-a(18) added by _Michel Marcus_, Sep 10 2019
%E a(19) from _Daniel Suteu_, Sep 10 2019
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