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A246719 Smallest natural number m for which there are exactly n distinct values k such that 0 < k < m^2 and 2^k - 1 is divisible by m^2.

%I A246719 #28 Dec 27 2021 10:38:46
%S A246719 1,3,7,15,113,65,31,91,73,39,21,331,267,55,217,435,203,697,127,703,
%T A246719 565,429,451,231,595,253,105,327,171,1045,1335,255,385,497,341,1295,
%U A246719 219,455,155,1417,969,165,2143,861,357,453,555,2821,195,1477,301,205,2091
%N A246719 Smallest natural number m for which there are exactly n distinct values k such that 0 < k < m^2 and 2^k - 1 is divisible by m^2.
%C A246719 Smallest odd number of the form 2q - 1 such that A246702(q) = n.
%C A246719 Additional terms include: a(426) = 1705, a(451) = 903, a(516) = 2067, a(536) = 2145, a(563) = 2255, a(566) = 2265, a(593) = 2373, a(761) = 3045, a(770) = 3081, a(786) = 2359, a(1333) = 2667, and a(3282) = 1093. - _Kevin P. Thompson_, Nov 26 2021
%H A246719 Kevin P. Thompson, <a href="/A246719/a246719.txt">Table of n, a(n) for n = 0..350</a>, with missing terms.
%e A246719 The first occurrence of 3 in the sequence A246702 occurs at n = 8. Therefore, a(3) = 2n - 1 = 2*8 - 1 = 15.
%t A246719 NumK[m_]:=NumK[m]=(m2=m^2;nk=0;Do[If[Mod[2^i,m2]==1,nk++],{i,m2-1}];nk)
%t A246719 nterms=10;Table[m=0;While[NumK[++m]!=n];m,{n,0,nterms-1}] (* _Paolo Xausa_, Nov 30 2021 *)
%o A246719 (PARI) isok(m, n) = {my(v = vector(m^2-1, k, Mod(2, m^2)^k == 1)); vecsum(v) == n;}
%o A246719 a(n) = {my(m=1); while (!isok(m, n), m++); m;} \\ _Michel Marcus_, Nov 27 2021
%Y A246719 Cf. Numbers of the form 2n - 1 such that A246702(n) = i: number 1 (i = 0), A167791 (i = 1), A246717 (i = 2), A246755 (i = 3).
%K A246719 nonn
%O A246719 0,2
%A A246719 _Juri-Stepan Gerasimov_, Nov 15 2014
%E A246719 Name corrected by _Antti Karttunen_, Nov 18 2014
%E A246719 Multiple corrections and new terms a(17)-a(52) from _Kevin P. Thompson_, Nov 26 2021