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A317670 Numbers k such that sigma_0(k-1) + sigma_0(k) + sigma_0(k+1) = 10, where sigma_0(k) = A000005(k).

%I A317670 #29 Jan 11 2022 02:17:06
%S A317670 7,12,14,18,22,38,58,158,178,382,502,542,718,878,1202,1318,1382,1438,
%T A317670 1622,1822,2018,2558,2578,2858,2902,3062,3118,3778,4282,4358,4442,
%U A317670 4678,4702,5078,5098,5582,5638,5702,5938,6338,6638,6662,6718,6998,7418,8222,8782,8818,9182,9662,9902
%N A317670 Numbers k such that sigma_0(k-1) + sigma_0(k) + sigma_0(k+1) = 10, where sigma_0(k) = A000005(k).
%C A317670 Besides the 1st, 2nd, and 4th terms, a(n) is 2 times a prime, one of a(n)-1 or a(n)+1 is a prime, and the other number is 3 times a prime.
%C A317670 The 10 in the definition is the smallest value for which this is a possibly infinite list.
%H A317670 Robert Israel, <a href="/A317670/b317670.txt">Table of n, a(n) for n = 1..10000</a>
%e A317670 For a(3)=14, sigma_0(13)=2, sigma_0(14)=4, and sigma_0(15)=4, hence sigma_0(a(3)-1) + sigma_0(a(3)) + sigma_0(a(3)+1) = 10.
%p A317670 Res:= 7,12,14,18: count:= 4:
%p A317670 p:= 9:
%p A317670 while count < 100 do
%p A317670   p:= nextprime(p);
%p A317670   n:= 2*p;
%p A317670   if n mod 3 = 1 then v:= isprime(n+1) and isprime((n-1)/3)
%p A317670   else v:= isprime(n-1) and isprime((n+1)/3)
%p A317670   fi;
%p A317670   if v then count:= count+1; Res:= Res, n fi
%p A317670 od:
%p A317670 Res; # _Robert Israel_, Aug 27 2018
%t A317670 Select[Partition[Range[10^4], 3, 1], Total@ DivisorSigma[0, #] == 10 &][[All, 2]] (* _Michael De Vlieger_, Aug 05 2018 *)
%o A317670 (PARI) isok(n) = numdiv(n-1) + numdiv(n) + numdiv(n+1) == 10; \\ _Michel Marcus_, Aug 04 2018
%Y A317670 Cf. A000005.
%K A317670 nonn
%O A317670 1,1
%A A317670 _Kevin D. Woerner_, Aug 03 2018