A160453 Numbers k which have a prime divisor p such that 1 is the only positive integer which divides k/p^m and is congruent to 1 modulo p, where p^(m+1) does not divide k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78

Offset: 1

Author

Masahiko Shin, May 14 2009

Keywords

• nonn

Comments

The solvability of a group whose order is a(n) can be reduced to the solvability of smaller group using the Sylow theorems, provided the order is not a prime.

80 is not a member of this sequence, but is a member of A168186. - Franklin T. Adams-Watters, Jan 26 2010

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

All three of A023805, A160453, A168186 are different.

Programs

PARI

is(k)=if(k<12,return(k>0));my(f=factor(k)); for(i=1,#f~, fordiv(k/f[i,1]^f[i,2],d, if(d>1&&d%f[i,1]==1,next(2))); return(1)); 0 \\ Charles R Greathouse IV, Oct 27 2013

Extensions

Corrected by Charles R Greathouse IV, Oct 27 2013