A323399 Sum of Jordan function J_2(n), A007434 and its Dirichlet inverse, A046970.

2, 0, 0, 9, 0, 48, 0, 45, 64, 144, 0, 120, 0, 288, 384, 189, 0, 240, 0, 360, 768, 720, 0, 408, 576, 1008, 640, 720, 0, 0, 0, 765, 1920, 1728, 2304, 888, 0, 2160, 2688, 1224, 0, 0, 0, 1800, 1920, 3168, 0, 1560, 2304, 1872, 4608, 2520, 0, 1968, 5760, 2448, 5760, 5040, 0, 1728, 0, 5760, 3840, 3069, 8064, 0, 0, 4320, 8448, 0, 0, 3480, 0, 8208, 4992, 5400

Offset: 1

Author

Antti Karttunen, Jan 13 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A007434, A046970.

Cf. also A319340, A322581, A323364.

Programs

PARI

A007434(n) = sumdiv(n, d, d*d*moebius(n/d));
A046970(n) = if(1==n,n,my(f=factor(n)); for(i=1, #f~, f[i,1] = 1-(f[i,1]^2)); factorback(f[,1]));
A323399(n) = (A007434(n) + A046970(n));

Formula

a(n) = A007434(n) + A046970(n).