A300236 Möbius transform of A032742 (the largest proper divisor of n).

1, 0, 0, 1, 0, 2, 0, 2, 2, 4, 0, 2, 0, 6, 4, 4, 0, 4, 0, 4, 6, 10, 0, 4, 4, 12, 6, 6, 0, 4, 0, 8, 10, 16, 6, 6, 0, 18, 12, 8, 0, 6, 0, 10, 8, 22, 0, 8, 6, 16, 16, 12, 0, 12, 10, 12, 18, 28, 0, 8, 0, 30, 12, 16, 12, 10, 0, 16, 22, 18, 0, 12, 0, 36, 16, 18, 10, 12, 0, 16, 18, 40, 0, 12, 16, 42, 28, 20, 0, 16, 12, 22, 30, 46, 18, 16, 0, 36

Offset: 1

Author

Antti Karttunen, Mar 10 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A008683, A032742, A300239.

Programs

Mathematica

Table[DivisorSum[n, # MoebiusMu[n/#]/FactorInteger[#][[1, 1]] &], {n, 98}] (* Michael De Vlieger, Mar 10 2018 *)

PARI

A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A300236(n) = sumdiv(n,d,moebius(n/d)*A032742(d));

Formula

a(n) = Sum_{d|n} A008683(n/d)*A032742(d).