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A354932 a(n) = 1/n * {the least k for which A345992(k) = n}.

%I A354932 #13 Jun 16 2022 10:26:25
%S A354932 1,3,4,5,3,7,4,3,5,11,3,13,7,5,4,7,3,19,4,7,11,9,3,7,13,9,4,17,3,31,4,
%T A354932 3,17,5,9,31,5,11,5,9,3,17,4,5,13,31,3,7,5,17,4,19,3,5,7,19,23,9,3,61,
%U A354932 8,7,8,5,11,19,4,23,7,47,3,29,7,5,19,9,13,47,4,7,13,11,3,17,16,23,4,23,3,13,4,31,11,5
%N A354932 a(n) = 1/n * {the least k for which A345992(k) = n}.
%C A354932 The first four terms that are not powers of primes are: a(112) = 15, a(122) = 35, a(145) = 33, a(155) = 12.
%C A354932 Question: Are 2, 3, 4, 6, 10, 12, 18, 30, 60 the only n such that a(n) = 1+n?
%H A354932 Antti Karttunen, <a href="/A354932/b354932.txt">Table of n, a(n) for n = 1..3349</a> (computed using million term data file provided for A344005 by _N. J. A. Sloane_)
%F A354932 a(n) = A354931(n) / n.
%t A354932 s[n_] := Module[{m = 1}, While[!Divisible[m*(m+1), n], m++]; GCD[n, m]]; a[n_] := Module[{k = n}, While[s[k] != n, k+=n]; k/n]; Array[a, 100] (* _Amiram Eldar_, Jun 15 2022 *)
%o A354932 (PARI)
%o A354932 A345992(n) = gcd(n,A344005(n));
%o A354932 A354932(n) = for(k=1,oo,if(A345992(k)==n,return(k/n)));
%Y A354932 Column 1 of A354940.
%Y A354932 Cf. A344005, A345992, A354931.
%K A354932 nonn
%O A354932 1,2
%A A354932 _Antti Karttunen_, Jun 14 2022