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A028235 If n = Product (p_j^k_j), a(n) = numerator of Sum 1/p_j (the denominator of this sum is A007947). 6
0, 1, 1, 1, 1, 5, 1, 1, 1, 7, 1, 5, 1, 9, 8, 1, 1, 5, 1, 7, 10, 13, 1, 5, 1, 15, 1, 9, 1, 31, 1, 1, 14, 19, 12, 5, 1, 21, 16, 7, 1, 41, 1, 13, 8, 25, 1, 5, 1, 7, 20, 15, 1, 5, 16, 9, 22, 31, 1, 31, 1, 33, 10, 1, 18, 61, 1, 19, 26, 59, 1, 5, 1, 39, 8, 21, 18, 71, 1, 7, 1, 43, 1, 41, 22, 45, 32 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
COMMENTS
For n=1, the empty sum = 0 = 0/1 = a(1)/A007947(1), thus a(1) should be 0. - Antti Karttunen, Mar 04 2018
LINKS
FORMULA
Fraction is additive with a(p^e) = 1/p.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A007947(k) = Sum_{p prime} 1/p^2 = 0.452247... (A085548). - Amiram Eldar, Sep 29 2023
EXAMPLE
Fractions begin with 0, 1/2, 1/3, 1/2, 1/5, 5/6, 1/7, 1/2, 1/3, 7/10, 1/11, 5/6, ...
MATHEMATICA
a[1] = 0; a[n_] := 1/FactorInteger[n][[All, 1]] // Total // Numerator;
Array[a, 100] (* Jean-François Alcover, May 08 2019 *)
PROG
(PARI) A028235(n) = numerator(vecsum(apply(p->(1/p), factor(n)[, 1]))); \\ Antti Karttunen, Mar 04 2018
CROSSREFS
Cf. A007947 (denominators), A085548.
Sequence in context: A358016 A250097 A340678 * A028236 A066504 A367202
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Erich Friedman.
Term a(1) changed to 0 by Antti Karttunen, Mar 04 2018
STATUS
approved

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)