A276984 Sum of squares of numbers less than n that do not divide n.

0, 0, 4, 9, 29, 41, 90, 119, 194, 255, 384, 440, 649, 765, 980, 1155, 1495, 1654, 2108, 2324, 2811, 3185, 3794, 4050, 4874, 5351, 6110, 6664, 7713, 8155, 9454, 10075, 11309, 12235, 13610, 14295, 16205, 17209, 18840, 19930, 22139, 23085, 25584, 26808, 29029, 30861, 33510, 34614, 37974, 39670

Offset: 1

Author

Ilya Gutkovskiy, Sep 29 2016

Keywords

• nonn
• easy

Examples

			a(3) = 4 because 3 has 2 divisors {1,3} therefore 1 non-divisor {2} and 2^2 = 4;
a(4) = 9 because 4 has 3 divisors {1,2,4} therefore 1 non-divisor {3} and 3^2 = 9;
a(5) = 29 because 5 has 2 divisors {1,5} therefore 3 non-divisors {2,3,4} and 2^2 + 3^2 + 4^2 = 29, etc.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000330, A001157, A024816, A049820.

Programs

Mathematica

Table[n (n + 1) ((2 n + 1)/6) - DivisorSigma[2, n], {n, 1, 50}]
Table[Total[Complement[Range[n],Divisors[n]]^2],{n,50}] (* Harvey P. Dale, May 10 2018 *)

PARI

a(n) = n*(n + 1)*(2*n + 1)/6 - sigma(n, 2); \\ Michel Marcus, Sep 29 2016

Formula

Dirichlet g.f.: (2 zeta(s-3) + 3*zeta(s-2) + zeta(s-1) - 6*zeta(s-2)*zeta(s))/6.

a(n) = n*(n + 1)*(2*n + 1)/6 - sigma_2(n).

a(n) = A000330(n) - A001157(n).