A028235 If n = Product (p_j^k_j), a(n) = numerator of Sum 1/p_j (the denominator of this sum is A007947).

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

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

Antti Karttunen, Table of n, a(n) for n = 1..65537

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

a(n) = A003415(A007947(n)) = A069359(A007947(n)). - Antti Karttunen, Jan 22 2025

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), A003415, A069359, A085548, A379967.

Sequence in context: A358016 A250097 A340678 * A028236 A066504 A367202

Adjacent sequences: A028232 A028233 A028234 * A028236 A028237 A028238

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Erich Friedman.

Term a(1) changed to 0 by Antti Karttunen, Mar 04 2018

Status

approved