A359883 a(n) = Sum_{d|n} d^(n-d) * (n/d)^d.
1, 3, 4, 21, 6, 367, 8, 5129, 19693, 106411, 12, 9590989, 14, 105614223, 2439477016, 8590983185, 18, 1788338285659, 20, 44174380774421, 1483406745548512, 584318428289047, 24, 2300697575522919961, 298023223876953151, 2481152876039086107
Offset: 1
Keywords
Crossrefs
Cf. A359882.
Programs
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Mathematica
a[n_] := DivisorSum[n, #^(n-#) * (n/#)^# &]; Array[a, 30] (* Amiram Eldar, Aug 09 2023 *)
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PARI
a(n) = sumdiv(n, d, d^(n-d)*(n/d)^d);
Formula
a(n) = [x^n] Sum_{k>0} (n * x / k)^k / (1 - (k * x)^k).
If p is prime, a(p) = 1 + p.