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A336643 Squarefree kernel of n divided by the squarefree part of n: a(n) = rad(n) / core(n). 2
1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 1, 5, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 2, 7, 5, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 5, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 7, 3, 10, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

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

FORMULA

a(n) = A007947(n) / A007913(n).

Multiplicative with a(p^k) = p^(1-(k mod 2)) = p^A059841(k).

MATHEMATICA

f[p_, e_] := p^(1 - Mod[e, 2]); a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Dec 07 2020 *)

PROG

(PARI) A336643(n) = (factorback(factorint(n)[, 1]) / core(n));

(PARI) A336643(n) = if(1==n, n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^(1-(f[i, 2]%2))));

CROSSREFS

Cf. A007913, A007947, A059841, A336644.

Sequence in context: A162154 A134505 A329376 * A334039 A076933 A071974

Adjacent sequences:  A336640 A336641 A336642 * A336644 A336645 A336646

KEYWORD

nonn,mult

AUTHOR

Antti Karttunen, Jul 28 2020

STATUS

approved

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Last modified September 19 09:35 EDT 2021. Contains 347556 sequences. (Running on oeis4.)