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A034460
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a(n) = usigma(n) - n, where usigma(n) = sum of unitary divisors of n (A034448).
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54
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0, 1, 1, 1, 1, 6, 1, 1, 1, 8, 1, 8, 1, 10, 9, 1, 1, 12, 1, 10, 11, 14, 1, 12, 1, 16, 1, 12, 1, 42, 1, 1, 15, 20, 13, 14, 1, 22, 17, 14, 1, 54, 1, 16, 15, 26, 1, 20, 1, 28, 21, 18, 1, 30, 17, 16, 23, 32, 1, 60, 1, 34, 17, 1, 19, 78, 1, 22, 27, 74, 1, 18, 1, 40, 29, 24, 19, 90, 1, 22, 1, 44
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,6
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ c * n^2, where c = (zeta(2)/zeta(3) - 1)/2 = 0.1842163888... . - Amiram Eldar, Feb 22 2024
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EXAMPLE
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Unitary divisors of 12 are 1, 3, 4, 12. a(12) = 1 + 3 + 4 = 8.
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MAPLE
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end proc:
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MATHEMATICA
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usigma[n_] := Sum[ If[GCD[d, n/d] == 1, d, 0], {d, Divisors[n]}]; a[n_] := usigma[n] - n; Table[ a[n], {n, 1, 82}] (* Jean-François Alcover, May 15 2012 *)
a[n_] := Times @@ (1 + Power @@@ FactorInteger[n]) - n; a[1] = 0; Array[a, 100] (* Amiram Eldar, Oct 03 2022 *)
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PROG
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(Haskell)
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CROSSREFS
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Cf. A063919 (essentially the same sequence).
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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