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A082344
Denominator of sopfr(n)/n, where sopfr=A001414 is the sum of prime factors (with repetition).
4
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
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
KEYWORD
nonn,frac
AUTHOR
Reinhard Zumkeller, Apr 09 2003
STATUS
approved