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A328414 Numbers k such that (Z/mZ)* = C_2 X C_(2k) has no solutions m, where (Z/mZ)* is the multiplicative group of integers modulo m.. 2
7, 12, 13, 17, 19, 25, 28, 31, 34, 37, 38, 43, 47, 49, 52, 57, 59, 61, 62, 67, 71, 73, 76, 77, 79, 80, 84, 85, 91, 92, 93, 94, 97, 100, 101, 103, 104, 107, 108, 109, 112, 117, 118, 121, 122, 124, 127, 129, 133, 137, 139, 142, 143, 144, 148, 149, 151, 152, 157, 160, 161, 163, 164 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Indices of 0 in A328410, A328411 and A328412.

By definition, if there is no such m that psi(m) = 2k, psi = A002322, then m is a term of this sequence.

LINKS

Table of n, a(n) for n=1..63.

Wikipedia, Multiplicative group of integers modulo n

EXAMPLE

12 is a term: if there exists m such that (Z/mZ)* = C_2 X C_24 = C_2 X C_8 X C_3, then m must have a factor q such that q is an odd prime power and phi(q) = 8 or phi(q) = 24, phi = A000010, which is impossible.

80 is a term: if there exists m such that (Z/mZ)* = C_2 X C_80 = C_2 X C_16 X C_5, then m must have a factor q such that q is an odd prime power and phi(q) = 80 or phi(q) = 16, which is impossible.

PROG

(PARI) isA328414(n) = my(r=4*n, N=floor(exp(Euler)*r*log(log(r^2))+2.5*r/log(log(r^2)))); for(k=r+1, N+1, if(eulerphi(k)==r && lcm(znstar(k)[2])==r/2, return(0)); if(k==N+1, return(1)))

for(n=1, 200, if(isA328414(n), print1(n, ", ")))

CROSSREFS

Cf. A328410, A328411, A328412. Complement of A328413.

Cf. also A000010, A002322, A005277, A079695.

Sequence in context: A070420 A223423 A274334 * A083681 A178660 A048653

Adjacent sequences:  A328411 A328412 A328413 * A328415 A328416 A328417

KEYWORD

nonn

AUTHOR

Jianing Song, Oct 14 2019

STATUS

approved

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Last modified June 20 12:34 EDT 2021. Contains 345164 sequences. (Running on oeis4.)