A091306 Sum of squares of unitary, squarefree divisors of n, including 1.
1, 5, 10, 1, 26, 50, 50, 1, 1, 130, 122, 10, 170, 250, 260, 1, 290, 5, 362, 26, 500, 610, 530, 10, 1, 850, 1, 50, 842, 1300, 962, 1, 1220, 1450, 1300, 1, 1370, 1810, 1700, 26, 1682, 2500, 1850, 122, 26, 2650, 2210, 10, 1, 5, 2900, 170, 2810, 5, 3172, 50, 3620
Offset: 1
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
-
Mathematica
f[p_, e_] := If[e == 1, p^2 + 1, 1]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Aug 30 2019*)
Formula
Multiplicative with a(p)=p^2+1 and a(p^e)=1 for e>1.
From Vaclav Kotesovec, Nov 20 2021: (Start)
Dirichlet g.f.: zeta(s) * zeta(s-2) * Product_{primes p} (1 + p^(4 - 3*s) - p^(2 - 2*s) - p^(4 - 2*s)).
Sum_{k=1..n} a(k) ~ c * zeta(3) * n^3 / 3, where c = Product_{primes p} (1 - 1/p^2 - 1/p^4 + 1/p^5) = 0.576152735385667059520611078264117275406247116802896188...
(End)
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