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A307042
Partial sums of the exponential divisors sum function: Sum_{k=1..n} esigma(k), where esigma is A051377.
5
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
1,2
LINKS
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.
FORMULA
a(n) ~ B * n^2, where B = 0.5682854937... (A275480).
MATHEMATICA
esigma[n_] := Times @@ (Sum[ First[#]^d, {d, Divisors[Last[#]]}] & ) /@ FactorInteger[n]; Accumulate[Array[esigma, 60]] (* after Jean-François Alcover at A051377 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Mar 21 2019
STATUS
approved