A383764 - OEIS

A383764

The largest unitary divisor of n that is an exponentially squarefree number.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 3, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68

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OFFSET

1,2

COMMENTS

First differs from A053165 at n = 32.

The number of these divisors is A383762(n) and their sum is A383763(n).

LINKS

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

FORMULA

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

a(n) <= A365683(n), with equality if and only if n is an exponentially squarefree number (A209061).

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

MATHEMATICA

f[p_, e_] := If[SquareFreeQ[e], p^e, 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)); }

CROSSREFS

Cf. A005117, A053165, A077610, A209061, A365683, A383762, A383763.

Sequence in context: A025483 A385007 A053165 * A056962 A043275 A216455

Adjacent sequences: A383761 A383762 A383763 * A383765 A383766 A383767

KEYWORD

nonn,easy,mult

AUTHOR

Amiram Eldar, May 09 2025

STATUS

approved