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A331970
The sum of the proper bi-unitary divisors of n.
4
0, 1, 1, 1, 1, 6, 1, 7, 1, 8, 1, 8, 1, 10, 9, 11, 1, 12, 1, 10, 11, 14, 1, 36, 1, 16, 13, 12, 1, 42, 1, 31, 15, 20, 13, 14, 1, 22, 17, 50, 1, 54, 1, 16, 15, 26, 1, 60, 1, 28, 21, 18, 1, 66, 17, 64, 23, 32, 1, 60, 1, 34, 17, 55, 19, 78, 1, 22, 27, 74, 1, 78, 1
OFFSET
1,6
COMMENTS
First differs from A126168 at n = 16.
LINKS
FORMULA
a(n) = A188999(n) - n.
EXAMPLE
a(6) = 6 since A188999(6) - 6 = 12 - 6 = 6.
MATHEMATICA
fun[p_, e_] := If[OddQ[e], (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1)-p^(e/2)]; bsigma[1] = 1; bsigma[n_] := bsigma[n] = Times @@ (fun @@@ FactorInteger[n]); bs[n_] := bsigma[n] - n; Array[bs, 100]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Feb 03 2020
STATUS
approved