A307042 Partial sums of the exponential divisors sum function: Sum_{k=1..n} esigma(k), where esigma is A051377.

1, 3, 6, 12, 17, 23, 30, 40, 52, 62, 73, 91, 104, 118, 133, 155, 172, 196, 215, 245, 266, 288, 311, 341, 371, 397, 427, 469, 498, 528, 559, 593, 626, 660, 695, 767, 804, 842, 881, 931, 972, 1014, 1057, 1123, 1183, 1229, 1276, 1342, 1398, 1458, 1509, 1587, 1640

Offset: 1

Author

Amiram Eldar, Mar 21 2019

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• J. Fabrykowski and M. V. Subbarao, The maximal order and the average order of multiplicative function sigma^(e)(n), in Théorie des nombres/Number theory (Quebec, PQ, 1987), 201-206, de Gruyter, Berlin, 1989.

Crossrefs

Cf. A024916, A051377, A064609, A275480.

Programs

Mathematica

esigma[n_] := Times @@ (Sum[ First[#]^d, {d, Divisors[Last[#]]}] & ) /@ FactorInteger[n]; Accumulate[Array[esigma, 60]] (* after Jean-François Alcover at A051377 *)

Formula

a(n) ~ B * n^2, where B = 0.5682854937... (A275480).