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A327172 If there is a divisor d of n such that phi(d)*d = n, then a(n) = d, otherwise a(n) = 0. 5

%I

%S 1,2,0,0,0,3,0,4,0,0,0,6,0,0,0,0,0,0,0,5,0,0,0,0,0,0,0,0,0,0,0,8,0,0,

%T 0,0,0,0,0,10,0,7,0,0,0,0,0,12,0,0,0,0,0,9,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,14,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,18,0,11,0,0,0,0,0,0,0,0,0,15

%N If there is a divisor d of n such that phi(d)*d = n, then a(n) = d, otherwise a(n) = 0.

%C If such a divisor exists, it is necessarily unique. See _Franz Vrabec_'s Dec 12 2012 comment in A002618.

%C Each natural number n > 0 occurs exactly once in this sequence, at position A002618(n).

%H Antti Karttunen, <a href="/A327172/b327172.txt">Table of n, a(n) for n = 1..21000</a>

%H Antti Karttunen, <a href="/A327172/a327172.txt">Data supplement: n, a(n) computed for n = 1..100000</a>

%F a(A002618(n)) = n.

%F a(A082473(n)) = A194507(n).

%t With[{s = EulerPhi /@ Range@ 120}, Table[DivisorSum[n, # &, # s[[#]] == n &], {n, Length@ s}]] (* _Michael De Vlieger_, Sep 29 2019 *)

%o (PARI) A327172(n) = { fordiv(n,d,if(eulerphi(d)*d == n, return(d))); (0); };

%Y Left inverse of A002618.

%Y Cf. A000010.

%Y Cf. A082473 (the indices of nonzero terms), A194507 (nonzero terms in the order of appearance).

%K nonn

%O 1,2

%A _Antti Karttunen_, Sep 28 2019

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Last modified June 15 11:44 EDT 2021. Contains 345048 sequences. (Running on oeis4.)