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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
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
Sequence in context: A099978 A242719 A242489 * A229308 A125075 A209983
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.)