A328421 Records in A317993.

2, 3, 4, 7, 8, 11, 12, 17, 30, 39, 52, 59

Offset

1,1

Comments

Companion sequence of A328420.

It seems that this sequence is infinite (i.e., A317993 is unbounded), but for each n, to really construct a number k such that A317993(k) > a(n) seems impossible.

Links

Table of n, a(n) for n=1..12.

Wikipedia, Multiplicative group of integers modulo n

Example

Let (Z/mZ)* be the multiplicative group of integers modulo m. We have (Z/mZ)* = (Z/104Z)* has 8 solutions, namely m = 104, 105, 112, 140, 144, 156, 180, 210; for all k' < 104, (Z/mZ)* = (Z/k'Z)* has fewer than 8 solutions. So A317993(104) = 8 is a term.

Prog

(PARI) b(n) = if(abs(n)==1||abs(n)==2, 2, my(i=0, k=eulerphi(n), N=floor(exp(Euler)*k*log(log(k^2))+2.5*k/log(log(k^2)))); for(j=k+1, N, if(znstar(j)[2]==znstar(n)[2], i++)); i)
my(t=0); for(k=1, 20000, if(b(k)>t, print1(b(k), ", "); t=b(k))) \\ Warning: program runs for about 30 min

Crossrefs

Cf. A317993, A328420.

Sequence in context: A368402 A284937 A271441 * A003508 A225229 A239389

Adjacent sequences: A328418 A328419 A328420 * A328422 A328423 A328424

Keyword

nonn,hard,more

Author

Jianing Song, Oct 14 2019

Status

approved