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A221048 The odd semiprime numbers (A046315) which are orders of a non-Abelian group. 1
21, 39, 55, 57, 93, 111, 129, 155, 183, 201, 203, 205, 219, 237, 253, 291, 301, 305, 309, 327, 355, 381, 417, 453, 471, 489, 497, 505, 543, 579, 597, 633, 655, 669, 687, 689, 723, 737, 755, 791, 813, 831, 849, 889, 905, 921, 939, 955, 979, 993, 1011, 1027, 1047 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers of the form pq where p,q are odd primes, p<q and q is congruent to 1 mod p.

The corresponding non-Abelian groups are the semidirect products of Z/qZ and Z/pZ. - Bernard Schott, May 16 2020

LINKS

Jinyuan Wang, Table of n, a(n) for n = 1..1000

S. K. Berberian, Non-Abelian Groups of Order pq, American Mathematical Monthly, Vol. 60, No. 1, Jan. 1953, 37-40.

MATHEMATICA

Select[1 + 2*Range[500], (f = FactorInteger[#]; Last /@ f == {1, 1} && Mod @@ Reverse[First /@ f] == 1) &] (* Giovanni Resta, Apr 14 2013 *)

PROG

(PARI) lista(nn) = {forstep(n=1, nn, 2, my(f=factor(n)); if ((#f~ == 2) && (vecmax(f[, 2]) == 1) && ((f[2, 1] % f[1, 1]) == 1), print1(n, ", ")); ); } \\ Michel Marcus, Sep 28 2017

(PARI) list(lim)=my(v=List()); if(lim<9, return([])); forprime(p=3, sqrtint(((lim\=1)-1)\2), forprimestep(q=2*p+1, lim, 2*p, listput(v, p*q))); Set(v) \\ Charles R Greathouse IV, Feb 08 2021

CROSSREFS

Intersection of A046315 and A060652.

Sequence in context: A072708 A338330 A102478 * A182297 A338552 A339002

Adjacent sequences:  A221045 A221046 A221047 * A221049 A221050 A221051

KEYWORD

nonn

AUTHOR

David Brown, Apr 14 2013

EXTENSIONS

More terms from Jinyuan Wang, May 16 2020

STATUS

approved

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Last modified June 28 18:38 EDT 2022. Contains 354907 sequences. (Running on oeis4.)