cp's OEIS Frontend

A247191 Number of prime divisors, counted with multiplicity, of A180202(n), the product of the two numbers in the n-th amicable pair, A002025(n) * A002046(n).

%I A247191 #12 Dec 13 2020 05:15:10
%S A247191 7,10,8,8,11,10,10,11,9,12,12,11,10,11,11,16,12,9,12,12,11,10,10,9,10,
%T A247191 11,12,11,12,12,11,11,11,11,11,11,11,11,13,11,13,11,10,10,9,13,12,12,
%U A247191 10,12,12,10,11,9,10,14,14,10,11,13,11,11,12,10,11,11,11
%N A247191 Number of prime divisors, counted with multiplicity, of A180202(n), the product of the two numbers in the n-th amicable pair, A002025(n) * A002046(n).
%C A247191 Motivated by Theorem 3. in P. Pollack paper stating: Fix a natural number k. Then there are only finitely many amicable pairs (N,M) for which Omega(N*M) <= k.
%H A247191 Amiram Eldar, <a href="/A247191/b247191.txt">Table of n, a(n) for n = 1..10000</a>
%H A247191 Paul Pollack, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.119.08.670">Finiteness Theorems for Perfect Numbers and Their Kin</a>, The American Mathematical Monthly, Vol. 119, No. 8 (October 2012), pp. 670-681
%F A247191 a(n) = A001222(A180202(n)).
%F A247191 a(n) = A001222(A002025(n) * A002046(n)).
%o A247191 (PARI) lista() = {va = readvec("b002025.txt"); vb = readvec("b002046.txt"); for (i=1, 80, print1(bigomega(va[i]*vb[i]), ", "));}
%Y A247191 Cf. A001222, A002025, A002046, A180202.
%K A247191 nonn
%O A247191 1,1
%A A247191 _Michel Marcus_, Nov 23 2014