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

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

1,2

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

Prog

(PARI) is(n)=if(n<12, return(n>0)); my(f=factor(n)); for(i=1, #f~, fordiv(n/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

Crossrefs

All three of A023805, A160453, A168186 are different.

Sequence in context: A353866 A085235 A364461 * A325778 A364531 A299702

Adjacent sequences: A160450 A160451 A160452 * A160454 A160455 A160456

Keyword

nonn

Author

Masahiko Shin, May 14 2009

Extensions

Corrected by Charles R Greathouse IV, Oct 27 2013

Status

approved