A379098 The waterproof hulls of numbers that are not waterproof (A379097).

180, 252, 360, 396, 468, 504, 612, 684, 720, 792, 828, 1400, 900, 936, 1575, 1008, 1044, 1116, 1224, 6300, 2200, 1332, 1368, 1440, 1476, 2475, 1548, 2600, 4752, 1656, 2800, 1692, 2925, 1764, 1800, 4312, 5616, 3150, 1908, 9900, 2016, 3400, 4851, 2088, 2124, 5096

Offset: 1

Author

Peter Luschny, Dec 16 2024

Keywords

• nonn

Comments

The waterproof hull h(k) of k is the smallest waterproof number that k divides. Zero and one are waterproof numbers by convention. Numbers that admit a prime factorization are waterproof if their water capacity is 0. (The water capacity of a number is defined in A275339.)

Crossrefs

Cf. A275339, A379095, A379096, A379097.

Programs

Python

# Using function "WaterCapacity" from A275339.
def s(n: int) -> int:
    j = n
    while True:
        if WaterCapacity(j) == 0 and j % n == 0: return j
        j += n
print([s(n) for n in range(1, 700) if WaterCapacity(n) > 0])