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

1,1

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.

Links

Table of n, a(n) for n=1..84.

Example

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).

Prog

(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])

Crossrefs

Cf. A275339, A379096, A379097, A379098.

Sequence in context: A053444 A175797 A358475 * A335550 A243129 A135717

Adjacent sequences: A379092 A379093 A379094 * A379096 A379097 A379098

Keyword

nonn,new

Author

Peter Luschny, Dec 16 2024

Status

approved