A074789 Partial sums of usigma(n)^2: square of the sum of unitary divisors of n.

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

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