A363013 - OEIS

A363013

a(n) is the number of prime factors (counted with multiplicity) of the n-th cubefull number (A036966).

0, 3, 4, 3, 5, 6, 4, 3, 7, 6, 5, 8, 3, 7, 9, 4, 7, 6, 8, 6, 10, 8, 3, 9, 8, 7, 11, 7, 3, 4, 9, 6, 5, 6, 10, 9, 8, 12, 3, 7, 10, 7, 9, 8, 3, 11, 10, 9, 13, 6, 8, 7, 11, 6, 8, 10, 3, 12, 4, 11, 6, 10, 14, 5, 7, 10, 6, 7, 9, 9, 12, 7, 9, 11, 3, 8, 9, 13, 7, 4, 3

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OFFSET

1,2

LINKS

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

Rafael Jakimczuk and Matilde Lalín, The Number of Prime Factors on Average in Certain Integer Sequences, Journal of Integer Sequences, Vol. 25 (2022), Article 22.2.3.

FORMULA

a(n) = A001222(A036966(n)).

a(n) >= 3, for n > 1.

Sum_{A036966(k) < x} a(k) = 3*c*x^(1/3)*log(log(x)) + (3*(B_2 - log(2)) + Sum_{p prime} ((4*p^(1/3)+5)/(p^(5/3)+p^(1/3)+1)))*c*x^(1/3) + O(x^(1/3)/sqrt(log(x))), where B_2 = A083342 and c = A362974 (Jakimczuk and Lalín, 2022). [corrected Sep 21 2024]

MATHEMATICA

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

PROG

(PARI) iscubefull(n) = n==1 || vecmin(factor(n)[, 2]) > 2;

apply(bigomega, select(iscubefull, [1..10000]))

CROSSREFS

Cf. A001222, A036966, A362974.

Similar sequences: A072047, A076399, A360729.

Sequence in context: A332026 A205692 A342927 * A226798 A045997 A360059

Adjacent sequences: A363010 A363011 A363012 * A363014 A363015 A363016

KEYWORD

nonn

AUTHOR

Amiram Eldar, May 13 2023

STATUS

approved