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A091306 Sum of squares of unitary, squarefree divisors of n, including 1. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If b(n,k) = sum of k-th powers of unitary, squarefree divisors of n, including 1, then b(n,k) is multiplicative with b(p,k)=p^k+1 and b(p^e,k)=1 for e>1.

Dirichlet g.f.: zeta(s)*product_{primes p} (1+p^(2-s)-p^(2-2s)). Dirichlet convolution of A000012 with the multiplicative sequence 1, 4, 9, -4, 25, 36, 49, 0, -9, 100, 121, -36, 169, 196,... - R. J. Mathar, Aug 28 2011

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

Multiplicative with a(p)=p^2+1 and a(p^e)=1 for e>1.

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*)

CROSSREFS

Cf. A056671, A092261.

Sequence in context: A258150 A099731 A307716 * A073048 A102258 A169841

Adjacent sequences:  A091303 A091304 A091305 * A091307 A091308 A091309

KEYWORD

mult,easy,nonn

AUTHOR

Vladeta Jovovic, Feb 23 2004

STATUS

approved

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Last modified October 20 16:08 EDT 2019. Contains 328268 sequences. (Running on oeis4.)