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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A023805 A168186 A085235 * A027855 A031996 A023753

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

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Last modified November 19 10:44 EST 2017. Contains 294936 sequences.