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

1,6

Comments

Numerator is A082343(n) = A001414(n)/A082299(n).

Links

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

Formula

a(n) = 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)=25, A082343(200)=2.

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 *)

Prog

(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

Crossrefs

Cf. A001414, A082299, A082343.

Sequence in context: A118740 A301431 A200302 * A021865 A198565 A190409

Adjacent sequences: A082341 A082342 A082343 * A082345 A082346 A082347

Keyword

nonn,frac

Author

Reinhard Zumkeller, Apr 09 2003

Status

approved