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

1,1

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

Links

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

Formula

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

Example

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

Prog

(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), ", ")));

Crossrefs

Cf. A001222, A002997, A135717.

Sequence in context: A161175 A356515 A095955 * A293431 A078573 A143786

Adjacent sequences: A272769 A272770 A272771 * A272773 A272774 A272775

Keyword

nonn

Author

Altug Alkan, May 06 2016

Status

approved