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 A034676 Sum of squares of unitary divisors of n. 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Unitary Divisor Function. Wikipedia, Unitary divisor. FORMULA 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 Sum_{k=1..n} a(k) ~ 30 * Zeta(3) * n^3 / Pi^4. - Vaclav Kotesovec, Jan 11 2019 Sum_{k>=1} 1/a(k) = 1.5594563610641446770272272038182777336348840179730233519185104374159616326... - Vaclav Kotesovec, Sep 20 2020 MATHEMATICA f[n_] := Block[{d = Divisors@ n}, Plus @@ (Select[d, GCD[#, n/#] == 1 &]^2)]; Array[f, 50] (* Robert G. Wilson v, Mar 04 2011 *) f[p_, e_] := p^(2*e)+1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 14 2020 *) PROG (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 CROSSREFS Cf. A034444, A034448, A034677, A034678-A034682. Cf. A077610. Sequence in context: A193053 A340047 A098749 * A076598 A306011 A080341 Adjacent sequences:  A034673 A034674 A034675 * A034677 A034678 A034679 KEYWORD nonn,mult AUTHOR STATUS approved

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Last modified May 20 00:55 EDT 2022. Contains 353847 sequences. (Running on oeis4.)