A272772 Number of prime divisors of (A002997(n) - 2) counted with multiplicity.

2, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 4, 1, 1, 3, 2, 3, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 3, 2, 1, 3, 2, 2, 1, 3, 1, 2, 3, 3, 4, 3, 2, 1, 2, 3, 2, 2, 2, 3, 3, 2, 2, 4, 1, 3, 3, 2, 4, 3, 2, 2, 2, 1, 2, 2, 3, 3, 2, 2, 2, 2, 4, 2, 1, 2, 2, 4, 2, 2, 2, 1, 3, 3, 2, 2, 2, 2, 3, 3, 2, 2, 3, 2, 1, 2, 2, 2, 4, 2, 2, 2, 4, 2

Offset: 1

Author

Altug Alkan, May 06 2016

Keywords

• nonn

Comments

62756641 is the first Carmichael number k such that k-2 has 5 prime divisors (counted with multiplicity).

What is the average value function of a(n) when n goes to infinity?

If these number act like typical numbers of their size, then standard heuristics suggest an average value of log log n since there are between x^(1/3) and x Carmichael numbers up to x for large enough x. - Charles R Greathouse IV, May 09 2016

Examples

			a(1) = 2 because 561 - 2 = 559 has 2 prime divisors that are 13 and 43.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A002997, A135717.

Programs

PARI

isA002997(n)=my(f); bittest(n, 0) && !for(i=1, #f=factor(n)~, (f[2, i]==1 && n%(f[1, i]-1)==1)||return) && #f>1
for(n=561, 1e7, if(isA002997(n), print1(bigomega(n-2), ", ")));

Formula

a(n) = A001222(A002997(n)-2).