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).

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, 11, 12, 11, 12, 12, 11, 11, 11, 11, 11, 11, 11, 11, 13, 11, 13, 11, 10, 10, 9, 13, 12, 12, 10, 12, 12, 10, 11, 9, 10, 14, 14, 10, 11, 13, 11, 11, 12, 10, 11, 11, 11

Offset: 1

Author

Michel Marcus, Nov 23 2014

Keywords

• nonn

Comments

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.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Paul Pollack, Finiteness Theorems for Perfect Numbers and Their Kin, The American Mathematical Monthly, Vol. 119, No. 8 (October 2012), pp. 670-681

Crossrefs

Cf. A001222, A002025, A002046, A180202.

Programs

PARI

lista() = {va = readvec("b002025.txt"); vb = readvec("b002046.txt"); for (i=1, 80, print1(bigomega(va[i]*vb[i]), ", "));}

Formula

a(n) = A001222(A180202(n)).

a(n) = A001222(A002025(n) * A002046(n)).