A384559 The sum of the exponential unitary (or e-unitary) divisors of n that are exponentially odd numbers (A268335).

1, 2, 3, 2, 5, 6, 7, 10, 3, 10, 11, 6, 13, 14, 15, 2, 17, 6, 19, 10, 21, 22, 23, 30, 5, 26, 30, 14, 29, 30, 31, 34, 33, 34, 35, 6, 37, 38, 39, 50, 41, 42, 43, 22, 15, 46, 47, 6, 7, 10, 51, 26, 53, 60, 55, 70, 57, 58, 59, 30, 61, 62, 21, 10, 65, 66, 67, 34, 69

Offset: 1

Author

Amiram Eldar, Jun 03 2025

Keywords

• nonn
• easy
• mult

Comments

First differs from A384558 at n = 512: a(512) = 514, while A384558(512) = 522.

The number of these divisors is A384557(n), and the largest of them is A331737(n).

Links

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

Crossrefs

Cf. A005117, A051377, A072587, A268335, A331737, A368979, A374459, A384557, A384558.

Programs

Mathematica

f[p_, e_] := DivisorSum[e, p^# &, OddQ[#] && CoprimeQ[#, e/#] &]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

PARI

a(n) = {my(f = factor(n)); prod(i = 1, #f~, sumdiv(f[i,2], d, (d % 2) * (gcd(d, f[i,2]/d) == 1) * f[i,1]^d));}

Formula

Multiplicative with a(p^e) = Sum_{d|e, d odd, gcd(d, e/d) = 1} p^d.

a(n) = n if and only if n is squarefree (A005117).

a(n) < n if and only if n is in A072587.

a(n) > n if and only if n is in A374459.