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URL: https://oeis.org/A393574

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A393574
Lesser of two consecutive 5-smooth numbers that are coprime.
2
1, 2, 3, 4, 5, 8, 9, 15, 24, 25, 80, 125, 128, 243, 2025, 3072, 15552, 16384, 19683, 32768, 78125, 390625, 1594323, 66430125, 128000000, 1220703125, 4271484375, 6103515625, 10460353203, 31250000000, 274658203125, 7625597484987, 19042491875328, 9007199254740992
OFFSET
1,2
COMMENTS
Subsequence of A051037 \ A143207. - Chai Wah Wu, Mar 11 2026
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..86 (terms 1..72 from Michael De Vlieger)
EXAMPLE
Let s = A051037 and b = A393575.
Table of n, a(n), and b(n) for select n:
n a(n) b(n)
---------------------------------------------------
1 s(1) = 1 = 1 2 = 2
2 s(2) = 2 = 2 3 = 3
3 s(3) = 3 = 3 4 = 2^2
4 s(4) = 4 = 2^2 5 = 5
5 s(5) = 5 = 5 6 = 2 * 3
6 s(7) = 8 = 2^3 9 = 3^2
10 s(16) = 25 = 5^2 27 = 3^3
11 s(30) = 80 = 2^4 * 5 81 = 3^4
12 s(37) = 125 = 5^3 128 = 2^7
13 s(38) = 128 = 2^7 135 = 3^3 * 5
14 s(50) = 243 = 3^5 250 = 2 * 5^3
15 s(109) = 2025 = 3^4 * 5^2 2048 = 2^11
MATHEMATICA
nn = 2^10; s = Union@ Flatten@ Table[2^a * 3^b * 5^c, {a, 0, nn}, {b, 0, Log[3, nn/2^a]}, {c, 0, Log[5, nn/(2^a*3^b)] } ]; Select[Partition[s, 2, 1], CoprimeQ @@ # &][[;; , 1]]
PROG
(Python) # uses code in A051037
from math import gcd
from itertools import islice, pairwise
def agen(): yield from (a for a, b in pairwise(A051037gen()) if gcd(a, b) == 1)
print(list(islice(agen(), 34))) # Michael S. Branicky, Feb 22 2026
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Feb 22 2026
STATUS
approved