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 A351166 a(1)=1; for n > 1, a(n) is the smallest number that has n divisors and is coprime to a(n-1). 0
 1, 2, 9, 8, 81, 20, 729, 40, 441, 80, 59049, 140, 531441, 320, 3969, 440, 43046721, 700, 387420489, 560, 88209, 5120, 31381059609, 1120, 1185921, 20480, 53361, 4160, 22876792454961, 2800, 205891132094649, 3080, 9979281, 327680, 1750329, 8800, 150094635296999121 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For every odd prime p, a(p) = 3^(p-1). For n > 1, the smallest prime factor of a(n) is 2 + (n mod 2); see Examples. For n > 4, a(n) is a multiple of 5 iff n is even. Is 4 the largest composite m such that a(m) is a prime power? LINKS Table of n, a(n) for n=1..37. EXAMPLE Given that a(27) = 53361 = 3^2 * 7^2 * 11^2, the prime factors of a(28) cannot include 3, 7, or 11, so the smallest primes available as prime factors of a(28) are 2, 5, and 13. The only prime signatures yielding 28 divisors are p^27, p^13 * q, p^6 * q^3, and p^6 * q * r, and the smallest candidate value with each of these signatures is 2^27 = 134217728, 2^13 * 5 = 40960, 2^6 * 5^3 = 8000, and 2^6 * 5 * 13 = 4160. The smallest of these is 4160, so a(28) = 4160. (This is the smallest term that is a multiple of 13.) The table below lists the first several terms and their prime factorizations. n a(n) -- ---- 1 1 = 1 2 2 = 2^1 3 9 = 3^2 4 8 = 2^3 5 81 = 3^4 6 20 = 2^2 * 5^1 7 729 = 3^6 8 40 = 2^3 * 5^1 9 441 = 3^2 * 7^2 10 80 = 2^4 * 5^1 CROSSREFS Cf. A000005. Sequence in context: A214300 A092397 A272348 * A092270 A249225 A191351 Adjacent sequences: A351163 A351164 A351165 * A351167 A351168 A351169 KEYWORD nonn AUTHOR Jon E. Schoenfield, Mar 27 2022 STATUS approved

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Last modified May 30 13:54 EDT 2023. Contains 363050 sequences. (Running on oeis4.)