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A082473 Numbers n such that n = phi(x)*core(x) for some x <= n, where phi(x) is the Euler totient function and core(x) the squarefree part of x. 7
1, 2, 6, 8, 12, 20, 32, 40, 42, 48, 54, 84, 108, 110, 120, 128, 156, 160, 192, 220, 240, 252, 272, 312, 336, 342, 432, 486, 500, 504, 506, 512, 544, 640, 660, 684, 768, 812, 840, 880, 930, 936, 960, 972, 1000, 1012, 1080, 1248, 1320, 1332, 1344, 1624, 1632 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also numbers n such that n = y*phi(y) for a unique positive integer y (see A194507). - Franz Vrabec, Aug 27 2011

Sequence A002618 sorted into ascending order; also A327171 sorted into ascending order, with duplicate terms removed.  Indices of nonzero terms in A327170 and in A327172. - Antti Karttunen, Sep 29 2019

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

From Antti Karttunen, Sep 29 2019: (Start)

a(n) = A002618(A194507(n)).

A327172(a(n)) = A194507(n).

(End)

MATHEMATICA

With[{nn = 1700}, TakeWhile[Union@ Array[EulerPhi[#] (Sqrt@ # /. (c_: 1) a_^(b_: 0) :> (c a^b)^2) &, nn], # <= nn &]] (* Michael De Vlieger, Sep 29 2019, after Bill Gosper at A007913 *)

PROG

(PARI) isok(n) = {for (x=1, n, if (eulerphi(x)*core(x) == n, return (1)); ); return (0); } \\ Michel Marcus, Dec 04 2013

CROSSREFS

Cf. A000010, A002618, A007913, A194507, A327170, A327171, A327172.

Sequence in context: A280236 A177869 A138639 * A325177 A263312 A226818

Adjacent sequences:  A082470 A082471 A082472 * A082474 A082475 A082476

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Apr 27 2003

STATUS

approved

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Last modified August 13 08:34 EDT 2020. Contains 336442 sequences. (Running on oeis4.)