A082344 Denominator of sopfr(n)/n, where sopfr=A001414 is the sum of prime factors (with repetition).

1, 1, 1, 1, 1, 6, 1, 4, 3, 10, 1, 12, 1, 14, 15, 2, 1, 9, 1, 20, 21, 22, 1, 8, 5, 26, 3, 28, 1, 3, 1, 16, 33, 34, 35, 18, 1, 38, 39, 40, 1, 7, 1, 44, 45, 46, 1, 48, 7, 25, 51, 52, 1, 54, 55, 56, 57, 58, 1, 5, 1, 62, 63, 16, 65, 33, 1, 68, 69, 5, 1, 6, 1, 74, 75, 76, 77, 13, 1, 80, 27, 82, 1, 6

Offset: 1

Author

Reinhard Zumkeller, Apr 09 2003

Keywords

• nonn
• frac

Comments

Numerator is A082343(n) = A001414(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)=25, A082343(200)=2.
		

Links

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

Crossrefs

Cf. A001414, A082299, A082343.

Programs

Mathematica

sopd[n_]:=Module[{f=Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[n]]}, Denominator[ Total[f]/n]]; Array[sopd,90] (* Harvey P. Dale, Jul 24 2018 *)
sopfr[n_] := If[n == 1, 0, Total[Times @@@ FactorInteger[n]]];
a[n_] := Denominator[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));
A082344(n) = (n/A082299(n)); \\ Antti Karttunen, Mar 04 2018

Formula

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