A283715 a(n) is the number of Carmichael numbers whose largest prime factor is prime(n).

0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 2, 2, 0, 0, 0, 0, 6, 3, 1, 9, 2, 0, 3, 9, 7, 3, 1, 16, 20, 42, 19, 12, 15, 3, 60, 54, 57, 2, 8, 2

Offset

1,7

Comments

Since Carmichael numbers are squarefree, there is only a finite number of them whose largest prime factor is any given prime.

Links

Table of n, a(n) for n=1..41.

Giovanni Resta, Carmichael numbers with largest prime factor <= 179, sorted by their largest prime factor

Example

a(28) = 1 because prime(28) = 107 and there is only one Carmichael number whose largest prime factor is 107, namely 413631505 = 5 * 7 * 17 * 73 * 89 * 107.

Mathematica

a[n_] := a[n] = If[n < 6, 0, Block[{t, p = Prime@ n}, Length@ Select[ Subsets[ Prime@ Range[2, n-1], {2, n-2}], (t = Times @@ #; Mod[t-1, p-1] == 0 && And @@ IntegerQ /@ ((p t - 1)/ (#-1))) &]]]; Array[a, 22]

Crossrefs

Cf. A002997, A081702, A280617.

Sequence in context: A027357 A256479 A277078 * A078808 A030363 A236460

Adjacent sequences: A283712 A283713 A283714 * A283716 A283717 A283718

Keyword

nonn,more

Author

Giovanni Resta, Mar 15 2017

Status

approved