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

1,4

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

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).

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]

Prog

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

Crossrefs

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

Sequence in context: A088440 A300253 A212173 * A274006 A203025 A057521

Adjacent sequences: A366990 A366991 A366992 * A366994 A366995 A366996

Keyword

nonn,easy,mult

Author

Amiram Eldar, Oct 31 2023

Status

approved