A271328 a(n) = A269347(3*n)/3.

1, 5, 10, 17, 28, 37, 50, 65, 82, 106, 122, 145, 170, 197, 228, 257, 294, 325, 362, 406, 442, 485, 530, 577, 628, 677, 730, 790, 842, 906, 962, 1025, 1090, 1161, 1228, 1297, 1376, 1445, 1522, 1606, 1682, 1765, 1850, 1937, 2028, 2117, 2210

Offset: 1

Author

Alec Jones, Apr 04 2016

Keywords

• easy
• nonn

Comments

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.

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

Links

• Alec Jones, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A269347, A271326.

Programs

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

Formula

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