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 A063959 #27 Aug 17 2025 19:37:19
%S A063959 0,0,2,10,100,1593,41741,1578242,80294846,5356015580,451223209946,
%T A063959 46900682786541,5891009442510166,879657744587755114,
%U A063959 153967535281046615774,31216213430872403460411,7256556722488434503836458,1917031284234466887065107947,571083301099266868435687532291
%N A063959 Sum of the primes from 1 to n!.
%C A063959 Sum of prime factors (without repetition) of (n!)!.
%H A063959 Amiram Eldar, <a href="/A063959/b063959.txt">Table of n, a(n) for n = 0..22</a> (extended using Kim Walisch's primesum; terms 0..20 from Daniel Suteu)
%H A063959 Kim Walisch, <a href="https://github.com/kimwalisch/primesum">primesum program</a>.
%F A063959 a(n) = A034387(A000142(n)). - _Michel Marcus_, Jun 14 2024
%e A063959 a(4) = sum of primes <= 24. They are 2, 3, 5, 7, 11, 13, 17, 19 and 23. This sum is 100.
%t A063959 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} ]
%t A063959 Do[ Print[ Sum[ Prime[k], {k, 1, PrimePi[n! ]}]], {n, 0, 10} ]
%t A063959 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 *)
%o A063959 (PARI)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!!)))
%Y A063959 Cf. A000142, A034387, A006990, A294194.
%K A063959 nonn
%O A063959 0,3
%A A063959 _Jason Earls_, Sep 03 2001
%E A063959 Better description and more terms from _Robert G. Wilson v_, Oct 04 2001
%E A063959 a(13)-a(15) from _Donovan Johnson_, May 03 2010
%E A063959 a(16)-a(18) from _Daniel Suteu_, Nov 15 2018