A160353 Numbers of the form p*q*r, where p < q < r are odd primes such that r = +/-1 (mod p*q).

435, 465, 861, 885, 903, 915, 1335, 1743, 2211, 2235, 2265, 2485, 2667, 2685, 2715, 3081, 3165, 3507, 3585, 3615, 4035, 4065, 4323, 4431, 4865, 4965, 5151, 5253, 5271, 5385, 5835, 5995, 6123, 6153, 6285, 6315, 6441, 6501, 6567, 6735, 7077, 7185, 7385

Offset

1,1

Comments

Kaplan (2007) has shown that this is a subsequence of A117223 (and thus of A160350; see there for the reference), i.e., the cyclotomic polynomial phi(n) has coefficients in {0,1,-1} for indices n listed here.

This is a subsequence of A160352 which drops the requirement that p > 2.

See A160350 for further details and references.

Links

Robin Visser, Table of n, a(n) for n = 1..10000

Example

a(1) = 435 = 3*5*29 is the smallest product of odd primes p < q < r such that r is congruent to +/- 1 modulo the product of the smaller factors, p*q.

Prog

(PARI) forstep( pqr=1, 9999, 2, my(f=factor(pqr)); #f~==3 & vecmax(f[, 2])==1 & abs((f[3, 1]+1)%(f[1, 1]*f[2, 1])-1)==1 & print1(pqr", "))

Crossrefs

Sequence in context: A145318 A054987 A054905 * A268475 A212227 A369153

Adjacent sequences: A160350 A160351 A160352 * A160354 A160355 A160356

Keyword

nonn

Author

M. F. Hasler, May 11 2009

Status

approved