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A327939
Multiplicative with a(p^e) = p^(e-(e mod p)).
12
1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 16, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 27, 4, 1, 1, 1, 16, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 16, 1, 1, 1, 4, 1, 27, 1, 4, 1, 1, 1, 4, 1, 1, 1, 64, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 16, 27, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 16, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 108, 1, 1, 1, 16
OFFSET
1,4
COMMENTS
Fixed points of the map x -> gcd(x, A003415(x)), i.e., if we start iterating with A085731 from any x = n (>= 1), we will eventually reach a(n), after which the result does not change anymore. This was found by LODA miner (see C. Krause link), and is easily seen to be true by Eric M. Schmidt's multiplicative formula for A085731. Note also that this sequence is idempotent, meaning a(a(n)) = a(n) for all n. - Antti Karttunen, Apr 05 2021
The largest divisor of n that is a term of A072873. - Amiram Eldar, Sep 14 2023
FORMULA
Multiplicative with a(p^e) = p^(e-(e mod p)).
a(n) = n / A327938(n).
MATHEMATICA
f[p_, e_] := p^(e - Mod[e, p]); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 14 2023 *)
PROG
(PARI) A327939(n) = { my(f = factor(n)); for(k=1, #f~, f[k, 2] = (f[k, 2]-(f[k, 2]%f[k, 1]))); factorback(f); };
CROSSREFS
Differs from A234957 for the first time at n=27.
Sequence in context: A365635 A276330 A234957 * A365837 A369669 A155826
KEYWORD
nonn,easy,mult
AUTHOR
Antti Karttunen, Oct 01 2019
STATUS
approved