OFFSET
0,3
COMMENTS
Sum of prime factors (without repetition) of (n!)!.
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.
FORMULA
EXAMPLE
a(4) = sum of primes <= 24. They are 2, 3, 5, 7, 11, 13, 17, 19 and 23. This sum is 100.
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} ]
PROG
(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!!)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Jason Earls, Sep 03 2001
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
STATUS
approved