The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A292367 Carmichael numbers c with record number of primes p such that c*p is also a Carmichael number. 0
 561, 1729, 41041, 1615681, 14676481, 40622401, 173085121, 367804801, 631071001, 8494657921, 138399075361, 432081216001, 997803878401, 3837165696001, 7599525373441, 42182344790209, 65032633451521, 186137387251201, 329797704600001, 2523853463040001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If c*p is a Carmichael number, where p is a prime, then (p-1)|(c-1), so given c, the number of possible primes is bounded by the number of divisors of c-1. The corresponding number of solutions is 0, 5, 7, 10, 12, 14, 18, 26, 30, 33, 55, 65, 71, 72, 90, 92, 112, 128, 192, 218. LINKS EXAMPLE 1729 has 5 prime numbers p: 37, 73, 109, 433 and 577, such that 1729*p: 63973, 126217, 188461, 748657 and 997633 are also Carmichael numbers. MATHEMATICA carmichaelQ[n_] := Not[PrimeQ[n]] && Divisible[n - 1, CarmichaelLambda[n]]; numSol[n_] := Module[{m = 0}, ds = Divisors[n-1]; Do[p = ds[[k]] + 1; If[! PrimeQ[p], Continue[]]; If[!carmichaelQ[p*n], Continue[]]; m++, {k, 1, Length[ds] - 1}]; m]; numSolmax=-1; seq={}; Do[n=A002997[[j]]; m=numSol[n]; If[m>numSolmax, AppendTo[seq, n]; numSolmax=m], {j, 1, Length[A002997]}]; seq CROSSREFS Cf. A002997. Sequence in context: A227976 A224930 A083732 * A290805 A217465 A097130 Adjacent sequences:  A292364 A292365 A292366 * A292368 A292369 A292370 KEYWORD nonn AUTHOR Amiram Eldar, Sep 15 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 26 17:27 EST 2020. Contains 331280 sequences. (Running on oeis4.)