A063959 Sum of the primes from 1 to n!.

0, 0, 2, 10, 100, 1593, 41741, 1578242, 80294846, 5356015580, 451223209946, 46900682786541, 5891009442510166, 879657744587755114, 153967535281046615774, 31216213430872403460411, 7256556722488434503836458, 1917031284234466887065107947, 571083301099266868435687532291

Offset: 0

Author

Jason Earls, Sep 03 2001

Keywords

• nonn

Comments

Sum of prime factors (without repetition) of (n!)!.

Examples

			a(4) = sum of primes <= 24. They are 2, 3, 5, 7, 11, 13, 17, 19 and 23. This sum is 100.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..22 (extended using Kim Walisch's primesum; terms 0..20 from Daniel Suteu)
• Kim Walisch, primesum program.

Crossrefs

Cf. A000142, A034387, A006990, A294194.

Programs

Mathematica

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 *)

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!!)))

Formula

a(n) = A034387(A000142(n)). - Michel Marcus, Jun 14 2024

Extensions

Better description and more terms from Robert G. Wilson v, Oct 04 2001

a(13)-a(15) from Donovan Johnson, May 03 2010

a(16)-a(18) from Daniel Suteu, Nov 15 2018