A363091 Sum of the divisor complements of the refactorable unitary divisors of n.
1, 3, 3, 4, 5, 9, 7, 9, 10, 15, 11, 13, 13, 21, 15, 16, 17, 30, 19, 20, 21, 33, 23, 28, 25, 39, 27, 28, 29, 45, 31, 32, 33, 51, 35, 41, 37, 57, 39, 46, 41, 63, 43, 44, 50, 69, 47, 48, 49, 75, 51, 52, 53, 81, 55, 64, 57, 87, 59, 66, 61, 93, 70, 64, 65, 99, 67, 68, 69, 105, 71
Offset: 1
Programs
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Mathematica
a[n_] := n*DivisorSum[n, 1/# &, CoprimeQ[#, n/#] && Divisible[#, DivisorSigma[0, #]] &]; Array[a, 100]
Formula
a(n) = n * Sum_{d|n, tau(d)|d, gcd(d,n/d)=1} 1 / d.