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A283715 a(n) is the number of Carmichael numbers whose largest prime factor is prime(n). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 17 12:00 EDT 2021. Contains 347477 sequences. (Running on oeis4.)