This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A077218 #22 Aug 28 2025 04:23:12
%S A077218 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,
%T A077218 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,
%U A077218 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
%N A077218 Sum of numbers of prime factors (counted with multiplicities) of numbers between n-th and (n+1)-st prime.
%C A077218 Also, number of prime factors (with multiplicity) of the product P(n) of the composite numbers between n-th and (n+1)-th prime.
%D A077218 Amarnath Murthy, Generalization of Partition function, Introducing Smarandache Factor Partition. Smarandache Notions Journal, Vol. 11, 2000.
%H A077218 T. D. Noe, <a href="/A077218/b077218.txt">Table of n, a(n) for n = 1..10000</a>
%F A077218 a(n) = Sum_{k=A000040(n)+1..A000040(n+1)-1} A001222(k). - _Reinhard Zumkeller_, Nov 29 2002
%e A077218 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. [corrected by _Harvey P. Dale_, May 25 2011]
%t A077218 Total[PrimeOmega[Range[First[#]+1,Last[#]-1]]]&/@Partition[Prime[ Range[90]],2,1] (* _Harvey P. Dale_, May 25 2011 *)
%Y A077218 Cf. A000040, A001222, A052297.
%K A077218 nonn,changed
%O A077218 1,2
%A A077218 _Amarnath Murthy_, Nov 03 2002
%E A077218 More terms and better description from _Reinhard Zumkeller_, Nov 29 2002