A365635 The largest divisor of n that is a term of A048102.

1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 27, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 27, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 27, 1, 1, 4, 1, 1

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Vaclav Kotesovec, Graphs - the asymptotic ratio (10^7, 10^8 and 10^9 terms).

Formula

Multiplicative with a(p^e) = 1 if e < p and p^p otherwise.

a(n) <= n with equality if and only if n is in A048102.

a(n) >= 1 with equality if and only if n is in A048103.

Dirichlet g.f.: zeta(s) * Product_{p prime} (1 + (p^p-1)/p^(p*s)).

Mathematica

f[p_, e_] := p^If[e < p, 0, p]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] < f[i, 1], 1, f[i, 1]^f[i, 1])); }

Crossrefs

Cf. A048102, A048103, A327939, A365634.

Sequence in context: A193512 A366524 A366523 * A276330 A234957 A327939

Adjacent sequences: A365632 A365633 A365634 * A365636 A365637 A365638

Keyword

nonn,easy,mult

Author

Amiram Eldar, Sep 14 2023

Status

approved