Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #6 Dec 20 2024 12:42:38
%S 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,
%T 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,
%U 3,3,5,3,15,3,5,5,9,7,3,7,21,9,5,3,15,5
%N The water sealings of numbers that are not waterproof (A379097).
%C 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.
%e 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).
%o (Python)
%o # Using function "WaterCapacity" from A275339.
%o def s(n: int) -> int:
%o j = n
%o while True:
%o if WaterCapacity(j) == 0 and j % n == 0: return j
%o j += n
%o print([s(n)//n for n in range(1, 1200) if WaterCapacity(n) > 0])
%Y Cf. A275339, A379096, A379097, A379098.
%K nonn
%O 1,1
%A _Peter Luschny_, Dec 16 2024