A379095 The water sealings of numbers that are not waterproof (A379097).

3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 3, 5, 3, 3, 3, 3, 15, 5, 3, 3, 3, 3, 5, 3, 5, 9, 3, 5, 3, 5, 3, 3, 7, 9, 5, 3, 15, 3, 5, 7, 3, 3, 7, 3, 3, 5, 5, 15, 3, 9, 7, 15, 3, 5, 3, 5, 3, 9, 5, 21, 5, 3, 7, 3, 3, 5, 3, 15, 3, 5, 5, 9, 7, 3, 7, 21, 9, 5, 3, 15, 5

Offset: 1

Author

Peter Luschny, Dec 16 2024

Keywords

• nonn

Comments

The water sealing of a number n is the smallest positive integer s(n) so that the water hull of n can be written h(n) = n * s(n). n is waterproof if and only if s(n) = 1.

Examples

			48300 has a water capacity of 17 and so is not waterproof. The waterproof hull of 48300 is 1014300. Thus the sealing of 48300 is 21. The prime factorization of the sealing shows where the water holes of n are, in this example at 3 and 7 (see the example in A275339).
		

Crossrefs

Cf. A275339, A379096, A379097, A379098.

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)//n for n in range(1, 1200) if WaterCapacity(n) > 0])