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

1,2

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

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.

Mathematica

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

Prog

(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)); }

Crossrefs

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

Sequence in context: A241592 A211506 A384558 * A182880 A182898 A133684

Adjacent sequences: A384556 A384557 A384558 * A384560 A384561 A384562

Keyword

nonn,easy,mult

Author

Amiram Eldar, Jun 03 2025

Status

approved