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A034676
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Sum of squares of unitary divisors of n.
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2
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1, 5, 10, 17, 26, 50, 50, 65, 82, 130, 122, 170, 170, 250, 260, 257, 290, 410, 362, 442, 500, 610, 530, 650, 626, 850, 730, 850, 842, 1300, 962, 1025, 1220, 1450, 1300, 1394, 1370, 1810, 1700, 1690, 1682, 2500, 1850, 2074, 2132, 2650, 2210, 2570, 2402, 3130
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OFFSET
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1,2
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COMMENTS
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Also sum of unitary divisors of n^2. - Vladeta Jovovic, Nov 13 2001
If b(n,k)=sum of k-th powers of unitary divisors of n then b(n,k) is multiplicative with b(p^e,k)=p^(k*e)+1. - Vladeta Jovovic, Nov 13 2001
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Unitary Divisor Function
Wikipedia, Unitary_divisor
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FORMULA
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Multiplicative with a(p^e)=p^(2*e)+1.
Dirichlet g.f. zeta(s)*zeta(s-2)/zeta(2*s-2). - R. J. Mathar, Mar 04 2011
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MATHEMATICA
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f[n_] := Block[{d = Divisors@ n}, Plus @@ (Select[d, GCD[#, n/#] == 1 &]^2)]; Array[f, 50] (* Robert G. Wilson v, Mar 04 2011 *)
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PROG
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(PARI) A034676_vec(len)={
a000012=direuler(p=2, len, 1/(1-X)) ;
a000290=direuler(p=2, len, 1/(1-p^2*X)) ;
a000290x=direuler(p=2, len, 1-p^2*X^2) ;
dirmul(dirmul(a000012, a000290), a000290x)
}
A034676_vec(70) ; /* via D.g.f., R. J. Mathar, Mar 05 2011 */
(Haskell)
a034676 = sum . map (^ 2) . a077610_row
-- Reinhard Zumkeller, Feb 12 2012
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CROSSREFS
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Cf. A034444, A034448, A034677, A034678-A034682.
Cf. A077610.
Sequence in context: A061409 A193053 A098749 * A076598 A080341 A086653
Adjacent sequences: A034673 A034674 A034675 * A034677 A034678 A034679
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KEYWORD
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nonn,mult
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AUTHOR
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Erich Friedman
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STATUS
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approved
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