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.
Table[Times @@ Table[Prime[i], {i, PrimePi[n!] + 1, PrimePi[(n + 1)!]}], {n, 0, 4}]
a(4) = sum of primes <= 24. They are 2, 3, 5, 7, 11, 13, 17, 19 and 23. This sum is 100.
NextPrim[n_] := (k = n + 1; While[ ! PrimeQ[k], k++ ]; k); s = 0; p = 1; Do[ Do[p = NextPrim[p]; s = s + p, {i, PrimePi[(n - 1)! ] + 1, PrimePi[(n)! ]}]; Print[s], {n, 1, 12} ]
Do[ Print[ Sum[ Prime[k], {k, 1, PrimePi[n! ]}]], {n, 0, 10} ]
Table[Total[Prime[Range[PrimePi[n!]]]],{n,0,9}] (* The program generates the first 10 terms of the sequence. *) (* Harvey P. Dale, Aug 17 2025 *)
sumprime(n,s,fac,i)=fac=factor(n); for(i=1,matsize(fac)[1],s=s+fac[i,1]); return(s); for(n=0,22,print(sumprime(n!!)))
a(3) = floor(log(7*11*13*17*19*23)) = floor(15.82) = 15.
Table[Floor[Plus @@ Table[Log[Prime[i]*1.], {i, PrimePi[n!] + 1, PrimePi[(n + 1)!]}]], {n, 2, 11}]
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