

A272772


Number of prime divisors of (A002997(n)  2).


0



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
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OFFSET

1,1


COMMENTS

62756641 is the first Carmichael number such that n2 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

Table of n, a(n) for n=1..105.


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(n2), ", ")));


CROSSREFS

Cf. A001222, A002997, A135717.
Sequence in context: A207676 A161175 A095955 * A293431 A078573 A143786
Adjacent sequences: A272769 A272770 A272771 * A272773 A272774 A272775


KEYWORD

nonn


AUTHOR

Altug Alkan, May 06 2016


STATUS

approved



