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 A074789 Partial sums of usigma(n)^2: square of the sum of unitary divisors of n. 4
 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; text; internal format)
 OFFSET 1,2 REFERENCES L. Toth, An asymptotic formula concerning the unitary divisor sum function, Stud. Univ. Babes-Bolyai, Math. 34, No. 2, 3-10 (1989). LINKS Vaclav Kotesovec, Table of n, a(n) for n = 1..10000 Vaclav Kotesovec, Graph - the asymptotic ratio 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*log(n)^4), alpha_1= Product_{p prime} (1+1/p^2-2/p^3-1/p^4-2/p^5+3/p^6), Zeta(2)=A013661 and Zeta(3)=A002117. MATHEMATICA Accumulate[Table[DivisorSum[n, # &, CoprimeQ[#, n/#] &]^2, {n, 1, 50}]] (* Vaclav Kotesovec, Feb 04 2019 *) CROSSREFS Cf. A034448, A064609. Cf. A057434, A061502, A072379. Sequence in context: A099978 A242719 A242489 * A229308 A125075 A209983 Adjacent sequences: A074786 A074787 A074788 * A074790 A074791 A074792 KEYWORD nonn AUTHOR Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Sep 07 2002 STATUS approved

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Last modified February 24 11:15 EST 2024. Contains 370303 sequences. (Running on oeis4.)