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

0,1

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.

Prog

(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

Crossrefs

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

Sequence in context: A350017 A000474 A291593 * A151578 A172227 A331352

Adjacent sequences: A029588 A029589 A029590 * A029592 A029593 A029594

Keyword

nonn

Author

David W. Wilson

Status

approved