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

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

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

Examples

			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, ...
		

Links

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

Crossrefs

Cf. A007947 (denominators), A003415, A069359, A085548, A379967.

Programs

Mathematica

a[1] = 0; a[n_] := 1/FactorInteger[n][[All, 1]] // Total // Numerator;
Array[a, 100] (* Jean-François Alcover, May 08 2019 *)

PARI

A028235(n) = numerator(vecsum(apply(p->(1/p), factor(n)[, 1]))); \\ Antti Karttunen, Mar 04 2018

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

Extensions

More terms from Erich Friedman.

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