A174172 Partials sums of A001694.

1, 5, 13, 22, 38, 63, 90, 122, 158, 207, 271, 343, 424, 524, 632, 753, 878, 1006, 1150, 1319, 1515, 1715, 1931, 2156, 2399, 2655, 2943, 3232, 3556, 3899, 4260, 4652, 5052, 5484, 5925, 6409, 6909, 7421, 7950, 8526, 9151, 9799, 10474, 11150, 11879, 12663

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Rafael Jakimczuk, The kernel of powerful numbers, International Mathematical Forum, Vol. 12, No. 15 (2017), pp. 721-730, Theorem 2.7, p. 729.

Formula

a(n) = Sum_{i=1..n} A001694(i).

a(n) ~ (zeta(3)^2/(3*zeta(3/2)^2)) * n^3. - Amiram Eldar, Jan 30 2023

a(n) = c * A001694(n)^(3/2) + o(A001694(n)^(3/2)), where c = zeta(3/2)/(3*zeta(3)) = 0.7244181041... (Jakimczuk, 2017). - Amiram Eldar, May 13 2023

Mathematica

Accumulate @ Select[Range[1000], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &] (* Amiram Eldar, Jan 30 2023 *)

Prog

(PARI) lista(kmax) = {my(s = 0); for(k = 1, kmax, if(k==1 || vecmin(factor(k)[, 2]) > 1, s += k; print1(s, ", "))); } \\ Amiram Eldar, May 13 2023

Crossrefs

Cf. A001694, A090699.

Sequence in context: A160170 A277189 A060004 * A076408 A006353 A155142

Adjacent sequences: A174169 A174170 A174171 * A174173 A174174 A174175

Keyword

nonn

Author

Jonathan Vos Post, Mar 10 2010

Status

approved