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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

62756641 is the first Carmichael number such that n-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

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(n-2), ", ")));

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

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Last modified June 21 17:44 EDT 2021. Contains 345365 sequences. (Running on oeis4.)