A327939 Multiplicative with a(p^e) = p^(e-(e mod p)).

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

Links

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

Christian Krause, LODA, an assembly language, a computational model and a tool for mining integer sequences.

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

Cf. A003415, A072873, A085731, A327938.

Differs from A234957 for the first time at n=27.

Sequence in context: A365635 A276330 A234957 * A365837 A369669 A155826

Adjacent sequences: A327936 A327937 A327938 * A327940 A327941 A327942

Keyword

nonn,easy,mult

Author

Antti Karttunen, Oct 01 2019

Status

approved