A300239 Difference between A032742 (the largest proper divisor of n) and its Möbius transform (A300236).

0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 4, 1, 5, 1, 6, 1, 1, 1, 8, 1, 1, 3, 8, 1, 11, 1, 8, 1, 1, 1, 12, 1, 1, 1, 12, 1, 15, 1, 12, 7, 1, 1, 16, 1, 9, 1, 14, 1, 15, 1, 16, 1, 1, 1, 22, 1, 1, 9, 16, 1, 23, 1, 18, 1, 17, 1, 24, 1, 1, 9, 20, 1, 27, 1, 24, 9, 1, 1, 30, 1, 1, 1, 24, 1, 29, 1, 24, 1, 1, 1, 32, 1, 13, 13, 30, 1, 35, 1, 28, 17

Offset

1,8

Links

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

Formula

a(n) = A032742(n) - A300236(n).

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

Mathematica

Table[n/FactorInteger[n][[1, 1]] - DivisorSum[n, # MoebiusMu[n/#]/FactorInteger[#][[1, 1]] &], {n, 105}] (* or *)
Fold[Function[{a, n}, Append[a, {Abs@ Total@ Map[MoebiusMu[n/#] a[[#, -1]] &, Most@ Divisors@ n], n/FactorInteger[n][[1, 1]]}]], {{0, 1}}, Range[2, 105]][[All, 1]] (* Michael De Vlieger, Mar 10 2018 *)

Prog

(PARI)
A032742(n) = if(1==n, n, n/vecmin(factor(n)[, 1]));
A300239(n) = -sumdiv(n, d, (d<n)*moebius(n/d)*A032742(d));

Crossrefs

Cf. A008683, A032742, A300236.

Sequence in context: A261960 A010121 A174726 * A354364 A299203 A329036

Adjacent sequences: A300236 A300237 A300238 * A300240 A300241 A300242

Keyword

nonn

Author

Antti Karttunen, Mar 10 2018

Status

approved