A348420 -id:A348420 - cp's OEIS frontend

A348418 a(n) is the smallest k with rank((Z/kZ)*) = n such that there are an odd number of coprime squares modulo k.

1, 3, 8, 24, 168, 1848, 35112, 807576, 25034856, 1076498808, 50595443976, 2985131194584, 200003790037128, 14200269092636088, 1121821258318250952, 93111164440414829016, 9590449937362727388648, 1026178143297811830585336, 130324624198822102484337672

Offset: 0

Jianing Song, Oct 18 2021

The rank of a finitely generated group rank(G) is defined to be the size of the minimal generating sets of G. In particular, rank((Z/kZ)*) = 0 if k <= 2 and A046072(k) otherwise.
The number of coprime squares modulo a(n) is given by A046073(a(n)) = A348420(n-2) for n >= 2.
a(n) is the least k such that the Sylow 2-subgroup of (Z/kZ)* is (C_2)^n. - Jianing Song, Aug 13 2023

			a(2) = 8;
a(3) = 8 * 3 = 24;
a(4) = 8 * 3 * 7 = 168;
a(5) = 8 * 3 * 7 * 11 = 1848;
a(6) = 8 * 3 * 7 * 11 * 19 = 35112.

Jianing Song, Table of n, a(n) for n = 0..200

Cf. A046072, A046073, A348420, A002145, A102476.

a(n) = if(n<=2, [1, 3, 8][n+1], my(t=8); forprime(p=2, , if(p%4==3, t*=p; if(n--<3, return(t))))) \\ following Charles R Greathouse IV's program for A078586

a(n) = 8 * A078586(n-2) = 8 * (Product_{k=1..n-2} A002145(k)) for n > 2.

cp's OEIS Frontend

A348418 a(n) is the smallest k with rank((Z/kZ)*) = n such that there are an odd number of coprime squares modulo k.

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