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 A118138 Sum of factorials of prime factors, with multiplicity. 1
 2, 6, 4, 120, 8, 5040, 6, 12, 122, 39916800, 10, 6227020800, 5042, 126, 8, 355687428096000, 14, 121645100408832000, 124, 5046, 39916802, 25852016738884976640000, 12, 240, 6227020802, 18, 5044 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS For primes p, a(p) = p!. For powers of primes a(p^k) = k*(p!). For nonsquare semiprimes A006881 = pq, we have a(pq)= p! + q!. For sphenic numbers A007304 = p * q * r we have a(pqr) = p! + q! + r!. See also A008472 the sum of the distinct primes dividing n. LINKS Eric Weisstein's World of Mathematics, Factorial Sums. FORMULA a(n) = SUM[p|n] p!. a(n) = SUM[i=1..k] e_i * (p_i)! where n = (p_1^e_1)*(p_2^e_2)*...*(p_k^e_k). EXAMPLE a(6) = 8 because 6 = 2 * 3 and 2! + 3! = 8. a(12) = 10 because 12 = 2^2 * 3 and 2! + 2! + 3! = 10. a(30) = 128 because 30 = 2 * 3 * 5 and 2! + 3! + 5! = 128. MATHEMATICA Table[Total[Flatten[PadRight[{}, Last[#], First[#]]&/@FactorInteger[ n]]!], {n, 30}] (* Harvey P. Dale, Jan 06 2012 *) PROG (PARI) a(n)=my(f=factor(n)); sum(i=1, #f~, f[i, 1]!*f[i, 2]) \\ Charles R Greathouse IV, Sep 14 2015 CROSSREFS Cf. A000040, A000142, A006881, A007304, A008472. Sequence in context: A022404 A210420 A306585 * A240023 A004583 A175995 Adjacent sequences:  A118135 A118136 A118137 * A118139 A118140 A118141 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, May 13 2006 STATUS approved

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)