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A056622 Square root of largest unitary square divisor of n. 4
1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 1, 5, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 4, 7, 5, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 8, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 5, 2, 1, 1, 1, 4, 9, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 7, 3, 10, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Unitary analog of A000188. These numbers are neither unitary nor necessarily square divisors.

Multiplicative because quotient of two multiplicative sequences. - Christian G. Bower, May 16 2005

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

FORMULA

a(n) = A000188(n)/A055229(n).

Multiplicative with a(p^e) = p^(e/2) if e even, a(p) = 1, and a(p^e) = p^((e-3)/2) for odd e > 1. - Amiram Eldar, Sep 14 2020

EXAMPLE

For n = 125: A000188(125) = 5, A055229(125) = 5, so a(125) = 1.

For n = 360: A000188(360) = 6, A055229(360) = 2, so a(360) = 3.

MATHEMATICA

Table[Sqrt@ SelectFirst[Reverse@ Divisors@ n, And[IntegerQ@ Sqrt@ #, CoprimeQ[#, n/#]] &], {n, 104}] (* Michael De Vlieger, Dec 06 2018 *)

f[p_, e_] := If[EvenQ[e], p^(e/2), If[e == 1, 1, p^((e - 3)/2)]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 14 2020 *)

PROG

(PARI)

A000188(n) = core(n, 1)[2]; \\ Michel Marcus, Feb 27 2013

A055229(n) = { my(c=core(n)); gcd(c, n/c); }; \\ Charles R Greathouse IV, Nov 20 2012

A056622(n) = (A000188(n)/A055229(n)); \\ Antti Karttunen, Nov 19 2017

CROSSREFS

Cf. A000188, A055229, A034444, A056623.

Sequence in context: A334039 A076933 A071974 * A331738 A306333 A237983

Adjacent sequences:  A056619 A056620 A056621 * A056623 A056624 A056625

KEYWORD

nonn,mult

AUTHOR

Labos Elemer, Aug 08 2000

STATUS

approved

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Last modified October 22 23:20 EDT 2021. Contains 348181 sequences. (Running on oeis4.)