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A272772
Number of prime divisors of (A002997(n) - 2) counted with multiplicity.
1
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
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
KEYWORD
nonn
AUTHOR
Altug Alkan, May 06 2016
STATUS
approved