A362971 - OEIS

%I #17 May 13 2023 06:17:31

%S 1,9,25,52,84,148,229,354,482,698,941,1197,1540,1972,2484,3109,3757,

%T 4486,5350,6350,7374,8670,10001,11729,13673,15673,17721,19908,22105,

%U 24506,27098,29842,32967,36342,39798,43686,47686,51782,56695,61695,66879,72367,78199

%N Partials sums of the cubefull numbers (A036966).

%H Amiram Eldar, <a href="/A362971/b362971.txt">Table of n, a(n) for n = 1..10000</a>

%H Rafael Jakimczuk, <a href="https://doi.org/10.12988/imf.2017.7759">The kernel of powerful numbers</a>, International Mathematical Forum, Vol. 12, No. 15 (2017), pp. 721-730, Theorem 2.7, p. 729.

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

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

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

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

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

%Y Cf. A036966, A174172, A362974.

%K nonn

%O 1,2

%A _Amiram Eldar_, May 13 2023