|
|
A319627
|
|
Primorial deflation of n (denominator): Let f be the completely multiplicative function over the positive rational numbers defined by f(p) = A034386(p) for any prime number p; f constitutes a permutation of the positive rational numbers; let g be the inverse of f; for any n > 0, a(n) is the denominator of g(n).
|
|
20
|
|
|
1, 1, 2, 1, 3, 1, 5, 1, 4, 3, 7, 1, 11, 5, 2, 1, 13, 2, 17, 3, 10, 7, 19, 1, 9, 11, 8, 5, 23, 1, 29, 1, 14, 13, 3, 1, 31, 17, 22, 3, 37, 5, 41, 7, 4, 19, 43, 1, 25, 9, 26, 11, 47, 4, 21, 5, 34, 23, 53, 1, 59, 29, 20, 1, 33, 7, 61, 13, 38, 3, 67, 1, 71, 31, 6
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
See A319626 for the corresponding numerators and additional comments.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
f(21/5) = (2*3) * (2*3*5*7) / (2*3*5) = 42, hence g(42) = 21/5 and a(42) = 5.
|
|
MATHEMATICA
|
Array[#2/GCD[#1, #2] & @@ {#, Apply[Times, Map[If[#1 <= 2, 1, NextPrime[#1, -1]]^#2 & @@ # &, FactorInteger[#]]]} &, 120] (* Michael De Vlieger, Aug 27 2020 *)
|
|
PROG
|
(PARI) a(n) = my (f=factor(n)); denominator(prod(i=1, #f~, my (p=f[i, 1]); (p/if (p>2, precprime(p-1), 1))^f[i, 2]))
|
|
CROSSREFS
|
Cf. A319626 (numerators, see comments there).
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|