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

1,1

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

Prog

(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

Crossrefs

Cf. A002997, A006972, A175530, A175531.

Subsequence of A120944.

Sequence in context: A217338 A217163 A243839 * A156846 A324711 A221053

Adjacent sequences: A287116 A287117 A287118 * A287120 A287121 A287122

Keyword

nonn

Author

Thomas Ordowski, May 20 2017

Extensions

More terms from Michel Marcus, May 20 2017

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

Status

approved