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A363318
Total distance from n to each of its refactorable unitary divisors.
0
0, 1, 2, 3, 4, 9, 6, 7, 8, 17, 10, 11, 12, 25, 14, 15, 16, 42, 18, 19, 20, 41, 22, 39, 24, 49, 26, 27, 28, 57, 30, 31, 32, 65, 34, 62, 36, 73, 38, 71, 40, 81, 42, 43, 80, 89, 46, 47, 48, 97, 50, 51, 52, 105, 54, 103, 56, 113, 58, 107, 60, 121, 116, 63, 64, 129, 66, 67, 68, 137, 70
OFFSET
1,3
FORMULA
a(n) = Sum_{d|n, tau(d)|d, gcd(d,n/d)=1} (n - d).
a(n) = n * A363298(n) - A363085(n).
MATHEMATICA
a[n_] := DivisorSum[n, n - # &, CoprimeQ[#, n/#] && Divisible[#, DivisorSigma[0, #]] &]; Array[a, 100]
CROSSREFS
Sequence in context: A222248 A352728 A236852 * A236837 A235042 A234742
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, May 27 2023
STATUS
approved