A029591 For n>0, a(n) is the least quasi-Carmichael number to base -n, extended to n=0 with the least composite squarefree integer.

6, 399, 598, 165, 1886, 715, 148219, 273, 343027, 231, 935, 3445, 4681203, 1547, 2821, 1105, 21098, 43183, 258482, 27071, 2117473, 3059, 10373, 2737, 690501, 1595, 23959, 42653, 1621007, 9331, 4169135, 35465, 543973, 14839, 36941, 1885, 4405589, 11063

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Comments

a(n) is the least squarefree composite integer, for which prime p | a(n) ==> p+n | a(n)+n.

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 399, p. 89, Ellipses, Paris 2008.

Links

• Donovan Johnson, Table of n, a(n) for n = 0..250
• J.-M. De Koninck, Those fascinating numbers, Entry 399, AMS, 2009.
• Index entries for sequences related to Carmichael numbers.

Crossrefs

Cf. A029590 (base n), A257750 (quasi-Carmichael numbers).

Programs

PARI

a(n) = {forcomposite (k=1, oo, if (issquarefree(k) && (omega(k) >= 2), my(f=factor(k)[,1]); my(ok = 1); for (j=1, #f, if ((k+n) % (f[j]+n), ok = 0; break);); if (ok, return (k));););} \\ Michel Marcus, Jan 09 2020