A362971 Partials sums of the cubefull numbers (A036966).

1, 9, 25, 52, 84, 148, 229, 354, 482, 698, 941, 1197, 1540, 1972, 2484, 3109, 3757, 4486, 5350, 6350, 7374, 8670, 10001, 11729, 13673, 15673, 17721, 19908, 22105, 24506, 27098, 29842, 32967, 36342, 39798, 43686, 47686, 51782, 56695, 61695, 66879, 72367, 78199

Offset: 1

Author

Amiram Eldar, May 13 2023

Keywords

• nonn

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.

Crossrefs

Cf. A036966, A174172, A362974.

Programs

Mathematica

Accumulate[Select[Range[10000], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 2 &]]

PARI

lista(kmax) = {my(s = 0); for(k = 1, kmax, if(k==1 || vecmin(factor(k)[, 2]) > 2, s += k; print1(s, ", ")));}

Formula

a(n) = Sum_{k=1..n} A036966(k).

a(n) = c * A036966(n)^(4/3) + o(A036966(n)^(4/3)), where c = A362974 / 4 = 1.1648165306... (Jakimczuk, 2017).

a(n) ~ c * n^4, where c = 1/(4 * A362974 ^ 3) = 0.002471652768... .