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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
OFFSET
1,8
LINKS
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 10 2018
STATUS
approved