A374981 a(n) = (n^2 - 1)/6 - Sum_{t=0..n-1} [ A000217(t)/n ], where [ x ] means the fractional part of x here.

0, 0, 1, 1, 3, 4, 6, 7, 11, 13, 16, 19, 24, 27, 33, 35, 42, 47, 53, 58, 67, 71, 78, 85, 95, 102, 112, 118, 128, 138, 147, 155, 170, 178, 191, 200, 213, 224, 238, 248, 263, 277, 290, 302, 322, 331, 347, 361, 380, 395, 413, 427, 445, 463, 482, 496, 519, 534, 554, 573, 594, 612, 637, 651, 678, 698

Offset: 1

Author

Thomas Scheuerle, Jul 26 2024

Keywords

• sign
• easy

Comments

a(c^n) for some constant c can be expressed as a linear recurrence with constant coefficients.

Crossrefs

Cf. A000217, A006095, A374968.

Programs

PARI

a(n) = (n^2-1)/6-sum(k=1,n,(k*(k+1)/2)%n)/n+((n+1)%2)/2

Formula

a(n) = (n^2 - 1 - A374968(n))/6.

a(2^n) = A006095(n).

a(3^n) has the ordinary generating function: x*(1 - 2*x + 5*x^2 + 12*x^3)/(1 - 13*x + 36*x^2 + 12*x^3 - 117*x^4 + 81*x^5).