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A074789
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Partial sums of usigma(n)^2: square of the sum of unitary divisors of n.
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0
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1, 10, 26, 51, 87, 231, 295, 376, 476, 800, 944, 1344, 1540, 2116, 2692, 2981, 3305, 4205, 4605, 5505, 6529, 7825, 8401, 9697, 10373, 12137, 12921, 14521, 15421, 20605, 21629, 22718, 25022, 27938, 30242, 32742, 34186, 37786, 40922, 43838
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| L. Toth, An asymptotic formula concerning the unitary divisor sum function, Stud. Univ. Babes-Bolyai, Math. 34, No. 2, 3-10 (1989).
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FORMULA
| a(n) = Sum_{k=1..n} usigma(k)^2 = Sum_{k=1..n} A034448(k)^2. Asymptotic expression: a(n) = Sum_{k<=n} usigma(k)^2 = (Zeta(2)*Zeta(3)*alpha_1/3)*n^3 + O(n^2*ln(n)^4), alpha_1= Product_{p prime} (1+1/p^2-2/p^3-1/p4-2/p^5+3/p^6), Zeta(2)=A013661 and Zeta(3)=A002117.
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CROSSREFS
| Cf. A034448, A064609.
Sequence in context: A137351 A134406 A099978 * A125075 A055710 A134420
Adjacent sequences: A074786 A074787 A074788 * A074790 A074791 A074792
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KEYWORD
| nonn
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AUTHOR
| Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Sep 07 2002
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