

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
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OFFSET

1,2


COMMENTS

Also numbers n such that n = y*phi(y) for an 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



