A287119 Squarefree composite numbers n such that p^2 - 1 divides n^2 - 1 for every prime p dividing n.

8569, 39689, 321265, 430199, 564719, 585311, 608399, 7056721, 11255201, 17966519, 18996769, 74775791, 75669551, 136209151, 321239359, 446660929, 547674049, 866223359, 1068433631, 1227804929, 1291695119, 2315403649, 2585930689, 7229159729, 7809974369, 8117634239

Offset: 1

Author

Thomas Ordowski, May 20 2017

Keywords

• nonn

Comments

Such numbers are odd and have at least three prime factors.

Problem: are there infinitely many such numbers?

Links

• Giovanni Resta, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A002997, A006972, A175530, A175531.

Subsequence of A120944.

Programs

PARI

isok(n) = {if (issquarefree(n) && !isprime(n), my(f = factor(n)); for (k=1, #f~, if ((n^2-1) % (f[k,1]^2-1), return (0));); return (1););} \\ Michel Marcus, May 20 2017

Extensions

More terms from Michel Marcus, May 20 2017

a(14)-a(26) from Giovanni Resta, May 20 2017