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A362971
Partials sums of the cubefull numbers (A036966).
1
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 13 2023
STATUS
approved