

A319627


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).


6



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
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OFFSET

1,3


COMMENTS

See A319626 for the corresponding numerators and additional comments.


LINKS

Daniel Suteu, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = A064989(n) / gcd(n, A064989(n)).
a(n) = 1 iff n belongs to A025487.


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(p1), 1))^f[i, 2]))


CROSSREFS

Cf. A025487, A064989, A319626.
Sequence in context: A131208 A168008 A178810 * A334990 A217668 A119479
Adjacent sequences: A319624 A319625 A319626 * A319628 A319629 A319630


KEYWORD

nonn,look,frac


AUTHOR

Rémy Sigrist, Sep 25 2018


STATUS

approved



