

A077218


Sum of numbers of prime factors (counted with multiplicities) of numbers between nth and (n+1)st prime.


4



0, 2, 2, 7, 3, 8, 3, 7, 14, 3, 15, 8, 3, 8, 15, 14, 4, 16, 8, 5, 13, 11, 14, 21, 10, 3, 9, 5, 10, 36, 12, 16, 3, 26, 4, 16, 17, 8, 16, 15, 5, 26, 7, 9, 4, 33, 30, 12, 4, 10, 14, 6, 29, 20, 14, 15, 5, 17, 10, 3, 28, 40, 9, 5, 9, 42, 16, 27, 4, 14, 13, 22, 17, 18, 8, 19, 22, 11, 23, 27, 5
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OFFSET

1,2


COMMENTS

Also, number of prime factors (with multiplicity) of the product P(n) of the composite numbers between nth 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

sum{A001222(k): A000040(n)<k < A000040(n+1)}.  Reinhard Zumkeller, Nov 29 2002


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

Cf. A052297
Sequence in context: A235709 A341760 A342453 * A102780 A227828 A115025
Adjacent sequences: A077215 A077216 A077217 * A077219 A077220 A077221


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



