A271328 - OEIS

%I #13 Apr 04 2016 16:00:40

%S 1,5,10,17,28,37,50,65,82,106,122,145,170,197,228,257,294,325,362,406,

%T 442,485,530,577,628,677,730,790,842,906,962,1025,1090,1161,1228,1297,

%U 1376,1445,1522,1606,1682,1765,1850,1937,2028,2117,2210

%N a(n) = A269347(3*n)/3.

%C a(n) is equal to n^2 + 1 with predictable regularity; in particular, the values of n for which a(n) does not equal n^2 + 1 are exactly those values n for which 3n is divisible by A269347(3*m) for some m with 1 < m < n. This is in part because 1 + sum{i=1...n}(2i - 1) = n^2 + 1; when computing a(n), each term has this form except when the named condition holds.

%C For example, a(5) does not equal 5^2 + 1 because 3(5) is divisible by A269347(6).

%H Alec Jones, <a href="/A271328/b271328.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A269347(3*n)/3.

%o (PARI) lista(nn) = {nn *= 3; va = vector(nn); va[1] = 1; for (n=2, nn, va[n] = sum(k=1, n-1, k*((n % va[k])==0)); ); vector(#va\3, n, va[3*n]/3); } \\ _Michel Marcus_, Apr 04 2016

%Y Cf. A269347, A271326.

%K easy,nonn

%O 1,2

%A _Alec Jones_, Apr 04 2016