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A361631
a(n) is the denominator of the median of the distinct prime factors of n.
3
1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1
OFFSET
2,5
LINKS
FORMULA
For p a prime, a(p^k) = 1.
EXAMPLE
a(12) = 2 since the distinct prime factors of 12 are 2 and 3, of median equal to 5/2.
a(30) = 1 since the distinct prime factors of 30 are 2, 3, and 5, of median equal to 3.
MATHEMATICA
a[n_]:=Denominator[Median[FactorInteger[n][[All, 1]]]]; Array[a, 88, 2]
PROG
(PARI) a(n)=my(f=factor(n)[, 1]~, i=length(f)); denominator(if(i%2, f[i\2+1], (f[i/2]+f[i/2+1])/2)) \\ Winston de Greef, Mar 23 2023
CROSSREFS
Cf. A001221, A027748, A323172, A361566, A361630 (numerator), A361633 (with multiplicity).
Sequence in context: A349163 A279495 A300409 * A247462 A323172 A327403
KEYWORD
nonn,frac
AUTHOR
Stefano Spezia, Mar 18 2023
STATUS
approved