cp's OEIS Frontend

A379096 Waterproof numbers >= 60.

%I A379096 #11 Dec 20 2024 12:42:46
%S A379096 61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,
%T A379096 85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,
%U A379096 106,107,108,109,110,111,112,113,114,115,116,117,118,119,121
%N A379096 Waterproof numbers >= 60.
%C A379096 All nonnegative numbers less than 60 are waterproof.
%C A379096 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.)
%C A379096 If the factors p_i^e_i in the canonical prime factorization of n are weakly ascending or weakly descending, then n is waterproof.
%C A379096 A number is waterproof if and only if it equals its waterproof hull (A379098). The waterproof hull h(n) of n is the smallest waterproof number that n divides.
%C A379096 Numbers that are not waterproof are listed in A379097.
%e A379096 Numbers having at most two distinct prime factors (A070915) are waterproof. The primorials (A002110) are waterproof.
%e A379096 48300 has a water capacity of 17 and so is not waterproof. The waterproof hull of 48300 is 1014300.
%p A379096 # The function 'water_capacity' is defined in A275339.
%p A379096 is_waterproof := n -> ifelse(n < 2, true, is(water_capacity(n) = 0)):
%p A379096 select(is_waterproof, [seq(60..121)]);
%o A379096 (Python)
%o A379096 # The function 'WaterCapacity' is defined in A275339.
%o A379096 print([n for n in range(60, 122) if WaterCapacity(n) == 0])
%Y A379096 Cf. A275339, A379094, A379095, A379097, A379098.
%K A379096 nonn
%O A379096 1,1
%A A379096 _Peter Luschny_, Dec 16 2024