OFFSET
1,2
COMMENTS
Also, number of prime factors (with multiplicity) of the product P(n) of the composite numbers between n-th and (n+1)-th prime.
REFERENCES
Amarnath Murthy, Generalization of Partition function, Introducing Smarandache Factor Partition. Smarandache Notions Journal, Vol. 11, 2000.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
FORMULA
EXAMPLE
a(6) = 8. Prime(6) = 13 and prime(7) = 17. 14, 15, and 16 are the composite numbers between 13 and 17. 14 has two prime factors (2 and 7); 15 has two prime factors (3 and 5); and 16 has four prime factors (2, 2, 2, and 2). Thus, a(6) = 2 + 2 + 4 = 8 total prime factors.
MATHEMATICA
Total[PrimeOmega[Range[First[#]+1, Last[#]-1]]]&/@Partition[Prime[ Range[90]], 2, 1] (* Harvey P. Dale, May 25 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Nov 03 2002
EXTENSIONS
More terms and better description from Reinhard Zumkeller, Nov 29 2002
Corrected example [from Harvey P. Dale, May 25 2011]
STATUS
approved