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A323384 Smallest number with exactly n divisors in Eisenstein integers. 0
1, 2, 3, 7, 9, 6, 27, 14, 12, 18, 243, 21, 729, 54, 36, 56, 6561, 60, 19683, 63, 108, 486, 177147, 42, 144, 1458, 147, 189, 4782969, 180, 14348907, 182, 972, 13122, 432, 84, 387420489, 39366, 2916, 126, 3486784401, 540, 10460353203, 1701, 441, 354294, 94143178827, 168, 1728, 720 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n) is the smallest k such that A319442(k) = n.
Analog of A005179 and A302252 over the ring of Eisenstein integers. The divisors are counted up to association.
LINKS
FORMULA
For primes p > 2, a(p) = 3^((p-1)/2).
EXAMPLE
Let w = (1 + sqrt(3)*i)/2, w' = (1 - sqrt(3)*i)/2.
The divisors of 14 in Eisenstein integers are 1, 2, 2 + w, 2 + w', 7, 4 + 2*w, 4 + 2*w', 14 and there associations, and 14 is the smallest number having exactly 8 divisors in Eisenstein integers, so a(8) = 14.
The divisors of 21 in Eisenstein integers are 1, 2*w - 1, 3, 2 + w, 2 + w', 5 - w, 5 - w', 6 + 3*w, 6 + 3*w', 7, 14*w - 7, 21 and there associations, and 21 is the smallest number having exactly 12 divisors in Eisenstein integers, so a(12) = 21.
PROG
(PARI)
a(n) = if(isprime(n)&&n>2, 3^((n-1)/2), my(k=1); while(A319442(k)!=n, k++); k)
CROSSREFS
Cf. A005179, A302252, A319442 (number of divisors of n in Eisenstein integers).
Sequence in context: A053960 A114056 A168222 * A349641 A140221 A046668
KEYWORD
nonn
AUTHOR
Jianing Song, Jan 12 2019
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)