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A370833 a(n) is the greatest prime dividing the n-th cubefree number, for n >= 2; a(1)=1. 3
1, 2, 3, 2, 5, 3, 7, 3, 5, 11, 3, 13, 7, 5, 17, 3, 19, 5, 7, 11, 23, 5, 13, 7, 29, 5, 31, 11, 17, 7, 3, 37, 19, 13, 41, 7, 43, 11, 5, 23, 47, 7, 5, 17, 13, 53, 11, 19, 29, 59, 5, 61, 31, 7, 13, 11, 67, 17, 23, 7, 71, 73, 37, 5, 19, 11, 13, 79, 41, 83, 7, 17, 43 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Jean-Marie De Koninck and Rafael Jakimczuk, Summing the largest prime factor over integer sequences, Revista de la Unión Matemática Argentina, Vol. 67, No. 1 (2024), pp. 27-35.
FORMULA
a(n) = A006530(A004709(n)).
Sum_{A004709(n) <= x} a(n) = Sum_{i=1..k} d_i * x^2/log(x)^i + O(x^2/log(x)^(k+1)), for any given positive integer k, where d_i are constants, d_1 = 315/(4*Pi^4) = 0.808446... (De Koninck and Jakimczuk, 2024).
MATHEMATICA
s[n_] := Module[{f = FactorInteger[n]}, If[AllTrue[f[[;; , 2]], # < 3 &], f[[-1, 1]], Nothing]]; Array[s, 200]
PROG
(PARI) lista(kmax) = {my(f); print1(1, ", "); for(k = 2, kmax, f = factor(k); if(vecmax(f[, 2]) < 3, print1(f[#f~, 1], ", "))); }
CROSSREFS
Sequence in context: A081812 A356427 A331634 * A341676 A139421 A219964
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Mar 03 2024
STATUS
approved

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Last modified June 19 15:28 EDT 2024. Contains 373503 sequences. (Running on oeis4.)