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.

1, 3, 7, 15, 113, 65, 31, 91, 73, 39, 21, 331, 267, 55, 217, 435, 203, 697, 127, 703, 565, 429, 451, 231, 595, 253, 105, 327, 171, 1045, 1335, 255, 385, 497, 341, 1295, 219, 455, 155, 1417, 969, 165, 2143, 861, 357, 453, 555, 2821, 195, 1477, 301, 205, 2091

Offset: 0

Author

Juri-Stepan Gerasimov, Nov 15 2014

Keywords

• nonn

Comments

Smallest odd number of the form 2q - 1 such that A246702(q) = n.

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

Examples

			The first occurrence of 3 in the sequence A246702 occurs at n = 8. Therefore, a(3) = 2n - 1 = 2*8 - 1 = 15.
		

Links

• Kevin P. Thompson, Table of n, a(n) for n = 0..350, with missing terms.

Crossrefs

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).

Programs

Mathematica

NumK[m_]:=NumK[m]=(m2=m^2;nk=0;Do[If[Mod[2^i,m2]==1,nk++],{i,m2-1}];nk)
nterms=10;Table[m=0;While[NumK[++m]!=n];m,{n,0,nterms-1}] (* Paolo Xausa, Nov 30 2021 *)

PARI

isok(m, n) = {my(v = vector(m^2-1, k, Mod(2, m^2)^k == 1)); vecsum(v) == n;}
a(n) = {my(m=1); while (!isok(m, n), m++); m;} \\ Michel Marcus, Nov 27 2021

Extensions

Name corrected by Antti Karttunen, Nov 18 2014

Multiple corrections and new terms a(17)-a(52) from Kevin P. Thompson, Nov 26 2021