A383763 The sum of unitary divisors of n that are exponentially squarefree numbers.

1, 3, 4, 5, 6, 12, 8, 9, 10, 18, 12, 20, 14, 24, 24, 1, 18, 30, 20, 30, 32, 36, 24, 36, 26, 42, 28, 40, 30, 72, 32, 33, 48, 54, 48, 50, 38, 60, 56, 54, 42, 96, 44, 60, 60, 72, 48, 4, 50, 78, 72, 70, 54, 84, 72, 72, 80, 90, 60, 120, 62, 96, 80, 65, 84, 144, 68

Offset

1,2

Comments

The number of these divisors is A383762(n) and the largest of them is A383764(n).

Links

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

Formula

Multiplicative with a(p^e) = p^e + 1 if e is squarefree (A005117), and 1 otherwise.

a(n) <= A034448(n), with equality if and only if n is an exponentially squarefree number (A209061).

a(n) <= A365682(n), with equality if and only if n is a squarefree number.

Mathematica

f[p_, e_] := If[SquareFreeQ[e], p^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~, if(issquarefree(f[i, 2]), f[i, 1]^f[i, 2]+1, 1)); }

Crossrefs

Cf. A005117, A034448, A077610, A209061, A365682, A383762, A383764.

Sequence in context: A378433 A378434 A385049 * A034448 A365211 A365172

Adjacent sequences: A383760 A383761 A383762 * A383764 A383765 A383766

Keyword

nonn,easy,mult

Author

Amiram Eldar, May 09 2025

Status

approved