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

1,2

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_{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... .

Mathematica

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

Prog

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

Crossrefs

Cf. A036966, A174172, A362974.

Sequence in context: A225322 A031162 A371085 * A348232 A147160 A336669

Adjacent sequences: A362968 A362969 A362970 * A362972 A362973 A362974

Keyword

nonn

Author

Amiram Eldar, May 13 2023

Status

approved