A082343 Numerator of sopfr(n)/n, where sopfr=A001414 is the sum of prime factors (with repetition).

0, 1, 1, 1, 1, 5, 1, 3, 2, 7, 1, 7, 1, 9, 8, 1, 1, 4, 1, 9, 10, 13, 1, 3, 2, 15, 1, 11, 1, 1, 1, 5, 14, 19, 12, 5, 1, 21, 16, 11, 1, 2, 1, 15, 11, 25, 1, 11, 2, 6, 20, 17, 1, 11, 16, 13, 22, 31, 1, 1, 1, 33, 13, 3, 18, 8, 1, 21, 26, 1, 1, 1, 1, 39, 13, 23, 18, 3, 1, 13, 4, 43, 1, 1, 22, 45, 32, 17

Offset: 1

Author

Reinhard Zumkeller, Apr 09 2003

Keywords

• nonn
• frac

Comments

Denominator is A082344(n) = n/A082299(n).

Examples

			n=200: (2+2+2+5+5)/(2*2*2*5*5) = 16/(2*2*2*5*5) = (2*2*2*2)/(2*2*2*5*5) = 2/25, therefore a(200)=2, A082344(200)=25.
		

Links

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

Crossrefs

Cf. A001414, A082299, A082344.

Programs

Mathematica

sopfr[n_] := If[n == 1, 0, Total[Times @@@ FactorInteger[n]]];
a[n_] := Numerator[sopfr[n]/n];
Array[a, 100] (* Jean-François Alcover, Dec 03 2021 *)

PARI

A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
A082299(n) = gcd(n, A001414(n));
A082343(n) = A001414(n)/A082299(n); \\ Antti Karttunen, Mar 04 2018

Formula

a(n) = A001414(n)/A082299(n).