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

1,6

Comments

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

Links

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

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A001414, A082299, A082344.

Sequence in context: A373363 A083345 A087262 * A166125 A199074 A343235

Adjacent sequences: A082340 A082341 A082342 * A082344 A082345 A082346

Keyword

nonn,frac

Author

Reinhard Zumkeller, Apr 09 2003

Status

approved