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 A289337 Composite numbers (pseudoprimes) n, that are not Carmichael numbers, such that A000670(n-1) == 0 (mod n). 1
 25, 125, 325, 451, 1561, 4089, 7107, 8625, 12025 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS I. J. Good proved that A000670(k*(p-1)) == 0 (mod p) for all k >= 1 and prime p. Therefore the congruence A000670(n-1) == 0 (mod n) holds for all primes and Carmichael numbers. This sequence consist of the other composite numbers for which the congruence holds. LINKS I. J. Good, The number of orderings of n candidates when ties are permitted, Fibonacci Quarterly, Vol. 13 (1975), pp. 11-18. EXAMPLE A000670(24) = 2958279121074145472650648875 is divisible by 25 and 25 is not a prime, nor a Carmichael number. MATHEMATICA a = 1; a[n_] := a[n] = Sum[Binomial[n, k]*a[n - k], {k, 1, n}]; carmichaelQ[n_]:=(Mod[n, CarmichaelLambda[n]] == 1); seqQ[n_] := !carmichaelQ[n] && Divisible[a[n-1], n]; Select[Range[2, 500], seqQ] CROSSREFS Cf. A000670, A002997, A289338. Sequence in context: A044738 A062672 A036321 * A211581 A226231 A211595 Adjacent sequences: A289334 A289335 A289336 * A289338 A289339 A289340 KEYWORD nonn,more AUTHOR Amiram Eldar, Jul 02 2017 STATUS approved

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Last modified January 31 20:46 EST 2023. Contains 359981 sequences. (Running on oeis4.)