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

Author

Amiram Eldar, Sep 14 2023

Keywords

• nonn
• easy
• mult

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).

Crossrefs

Cf. A048102, A048103, A327939, A365634.

Programs

Mathematica

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

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]));}

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)).