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A351913 Least k such that A352483(k) = n, or -1 if no such k exists.

%I A351913 #69 Aug 18 2022 11:47:28
%S A351913 3,9,5,204,7,876,20,140,11,492,13,776,32,904,17,441,19,23364,44,2178,
%T A351913 23,25,27,1544,216,3756,29,460,31,1928,35,2056,280,1644,37,5196,117,
%U A351913 162,41,1089,43,2696,92,2824,47,49,51,6924,153,812,53,7524,57,3464,116,1521,59,940,61
%N A351913 Least k such that A352483(k) = n, or -1 if no such k exists.
%C A351913 What is the value of a(102)?
%C A351913 Conjecture: a(102) and all "Unknown" values in the a-file equal -1. - _Paolo Xausa_, Aug 16 2022
%H A351913 Michel Marcus, <a href="/A351913/b351913.txt">Table of n, a(n) for n = 1..101</a>
%H A351913 Michel Marcus and Paolo Xausa, <a href="/A351913/a351913_1.txt">Table of n, a(n) for n = 1..10000</a> (with a(n) noted as Unknown when the value is not known; search up to 125*10^9).
%H A351913 Paolo Xausa, <a href="/A351913/a351913_1.pdf">Log-log scatterplot of a(n), n = 1..10000</a>, with unknown values (in orange) placed at the search limit (125*10^9).
%F A351913 a(n) = n+2 iff n > 0 is a term of A040976. - _Bernard Schott_, Mar 24 2022
%t A351913 a[n_] := Module[{k = 3}, While[Denominator[k*(d = DivisorSigma[0, k])/(k - d)] != n, k++]; k]; Array[a, 60] (* _Amiram Eldar_, Mar 18 2022 *)
%o A351913 (PARI) f(n) = my(d=numdiv(n)); denominator(n*d/(n-d)); \\ A352483
%o A351913 a(n) = {my(k=3); while (f(k) != n, k++); k;}
%o A351913 (Python)
%o A351913 from math import gcd
%o A351913 from sympy import divisor_count
%o A351913 from itertools import count, islice
%o A351913 def f(n): d = divisor_count(n); g = gcd(n-d, n*d); return (n-d)//g
%o A351913 def agen():
%o A351913     n, adict = 1, dict()
%o A351913     for k in count(1):
%o A351913         fk = f(k)
%o A351913         if fk not in adict: adict[fk] = k
%o A351913         while n in adict: yield adict[n]; n += 1
%o A351913 print(list(islice(agen(), 60))) # _Michael S. Branicky_, Jul 23 2022
%Y A351913 Cf. A000005, A040976, A049820, A146566, A352483.
%K A351913 nonn
%O A351913 1,1
%A A351913 _Michel Marcus_, Mar 18 2022