OFFSET
1,2
REFERENCES
József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory, Vol. 1, Springer, 2006, Chapter IV, p. 122.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1000
Paul Erdős and Aleksandar Ivić, Estimates for sums involving the largest prime factor of an integer and certain related additive functions, Studia Sci. Math. Hungar, Vol. 15, No. 1-3 (1980), pp. 183-199.
Paul Erdős and Aleksandar Ivić, On sums involving reciprocals of certain arithmetical functions, Publ. Inst. Math.(Beograd)(NS), Vol. 32, No. 46 (1982), pp. 49-56.
Paul Erdős, Aleksandar Ivić, and Carl Pomerance, On sums involving reciprocals of the largest prime factor of an integer, Glasnik Matematicki, Vol. 21, No. 41 (1986), pp. 283-300.
Aleksandar Ivić, Sum of reciprocals of the largest prime factor of an integer, Archiv der Mathematik, Vol. 36 (1981), pp. 57-61.
Aleksandar Ivić, On sums involving reciprocals of the largest prime factor of an integer II, Acta Arithmetica, Vol. 71, No. 3 (1995), pp. 229-251
Aleksandar Ivić and Carl Pomerance, Estimates for certain sums involving the largest prime factor of an integer, Coll. Math. Soc. J. Bolyai, Vol. 34 (1981), pp. 769-789.
FORMULA
a(n)/A378679(n) = n * exp(-sqrt(2*log(n)*log(log(n))) + O(sqrt(log(n)*log(log(log(n)))))) (Ivić, 1981).
EXAMPLE
Fractions begin: 1, 3/2, 11/6, 7/3, 38/15, 43/15, 316/105, 737/210, 269/70, 283/70, 3183/770, 10319/2310, ...
MATHEMATICA
Numerator@ Accumulate[Table[1/FactorInteger[n][[-1, 1]], {n, 1, 33}]]
PROG
(PARI) lista(nmax) = {my(s = 1); print1(1, ", "); for(n = 2, nmax, f = factor(n); s += 1/f[#f~, 1]; print1(numerator(s), ", ")); }
CROSSREFS
KEYWORD
nonn,easy,frac,new
AUTHOR
Amiram Eldar, Dec 03 2024
STATUS
approved