A318879 a(n) = Sum_{d|n} [d-(2*phi(d)) > 0]*(d-(2*phi(d))).

0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 6, 0, 2, 0, 0, 0, 8, 0, 6, 0, 2, 0, 14, 0, 2, 0, 6, 0, 18, 0, 0, 0, 2, 0, 24, 0, 2, 0, 14, 0, 22, 0, 6, 0, 2, 0, 30, 0, 12, 0, 6, 0, 26, 0, 14, 0, 2, 0, 54, 0, 2, 0, 0, 0, 30, 0, 6, 0, 26, 0, 56, 0, 2, 0, 6, 0, 34, 0, 30, 0, 2, 0, 66, 0, 2, 0, 14, 0, 66, 0, 6, 0, 2, 0, 62, 0, 16, 0, 36, 0, 42, 0, 14, 9

Offset: 1

Author

Antti Karttunen, Sep 05 2018

Keywords

• nonn

Examples

			n = 105 has divisors [1, 3, 5, 7, 15, 21, 35, 105]. When A083254 is applied to them, we obtain [1, 1, 3, 5, 1, 3, 13, -9]. Summing the negative numbers present, and negating, we get a(105) = -(-9) = 9.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000010, A033879, A083254, A318878.

Cf. also A318679.

Programs

PARI

A318879(n) = sumdiv(n,d,d=d-(2*eulerphi(d)); (d>0)*d);

Formula

a(n) = -Sum_{d|n} [A083254(d) < 0]*A083254(d), where A083254(n) = 2*phi(n) - n, and [ ] are the Iverson brackets.

a(n) = A318878(n) - A033879(n).