A366993 The largest divisor of n that is a term of A056166.

1, 1, 1, 4, 1, 1, 1, 8, 9, 1, 1, 4, 1, 1, 1, 8, 1, 9, 1, 4, 1, 1, 1, 8, 25, 1, 27, 4, 1, 1, 1, 32, 1, 1, 1, 36, 1, 1, 1, 8, 1, 1, 1, 4, 9, 1, 1, 8, 49, 25, 1, 4, 1, 27, 1, 8, 1, 1, 1, 4, 1, 1, 9, 32, 1, 1, 1, 4, 1, 1, 1, 72, 1, 1, 25, 4, 1, 1, 1, 8, 27, 1, 1, 4

Offset: 1

Author

Amiram Eldar, Oct 31 2023

Keywords

• nonn
• easy
• mult

Comments

The number of these divisors is A095691(n) and their sum is A366990(n).

Links

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

Crossrefs

Cf. A005117, A007917, A056166, A095691, A366988, A366990.

Programs

Mathematica

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

PARI

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

Formula

Multiplicative with a(p) = 1 and a(p^e) = p^A007917(e).

a(n) <= n, with equality if and only if n is in A056166.

a(n) >= 1, with equality if and only if n is squarefree (A005117).