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A307118 a(1) = 0; for n>1, a(n) = dr(n-1) + dr(n) + dr(n+1), where dr(n) is the number of nontrivial divisors of n (A070824).

%I A307118 #34 Aug 16 2019 16:16:29
%S A307118 0,0,1,1,3,2,4,3,5,3,6,4,6,4,7,5,7,4,8,6,8,4,8,7,9,5,8,6,10,6,10,6,8,
%T A307118 6,11,9,9,4,10,8,12,6,10,8,10,6,10,9,13,7,10,6,10,8,14,10,10,4,12,10,
%U A307118 12,6,11,11,13,8,10,6,12,8,16,10,12,6,10,10,12,8,14,11,13,5,12,12,14,6,10,8,16,12,16
%N A307118 a(1) = 0; for n>1, a(n) = dr(n-1) + dr(n) + dr(n+1), where dr(n) is the number of nontrivial divisors of n (A070824).
%C A307118 Real divisibility of n's one-area (or 1-area). This is the first step to examine the divisibility of n's k-area. n's k-area is the set of m for which |n-m| is less than or equal to k (where n, k, m are natural numbers). 1's 1-area is {1,2}, 5's 1-area {4,5,6}, 3's 2-area {1,2,3,4,5}. We could call this natural area, and still talk about nonnegative or integer areas, etc.
%t A307118 {0}~Join~MapAt[# + 1 &, Total /@ Partition[DivisorSigma[0, Range@ 82] - 2, 3, 1], 1] (* _Michael De Vlieger_, Jun 06 2019 *)
%o A307118 (PARI) dr(n) = if (n<2, 0, numdiv(n)-2);
%o A307118 a(n) = if (n==1, 0, dr(n-1) + dr(n) + dr(n+1)); \\ _Michel Marcus_, Apr 11 2019
%Y A307118 Cf. A070824, A307119, A307120.
%K A307118 nonn
%O A307118 1,5
%A A307118 _Todor Szimeonov_, Mar 25 2019