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A300239 Difference between A032742 (the largest proper divisor of n) and its Möbius transform (A300236). 4
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 (list; graph; refs; listen; history; text; internal format)
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 * A299203 A329036 A205552

Adjacent sequences:  A300236 A300237 A300238 * A300240 A300241 A300242

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 10 2018

STATUS

approved

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Last modified February 23 13:37 EST 2020. Contains 332159 sequences. (Running on oeis4.)