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 A025281 a(n) = sopfr(n!), where sopfr = A001414  is the integer log. 4
 0, 0, 2, 5, 9, 14, 19, 26, 32, 38, 45, 56, 63, 76, 85, 93, 101, 118, 126, 145, 154, 164, 177, 200, 209, 219, 234, 243, 254, 283, 293, 324, 334, 348, 367, 379, 389, 426, 447, 463, 474, 515, 527, 570, 585, 596, 621, 668, 679, 693, 705, 725, 742, 795, 806, 822, 835, 857, 888 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(0)=0; for n>0, a(n)=sum(k=1,n, A001414(k)). - Benoit Cloitre, Apr 14 2002 The subsequence of primes in this partial sum begins: 2, 5, 19, 101, 283, 293, 367, 379, 389, 463, 857, 947. - Jonathan Vos Post, Mar 08 2010 LINKS T. D. Noe, Table of n, a(n) for n = 0..1000 FORMULA a(n) = A001414(A000142(n)). Asymptotic formula: a(n)~(Pi^2/12)*n^2/log(n). - Benoit Cloitre, Apr 14 2002 MAPLE with(numtheory): P:=proc(n) local a, b, k; b:=ifactors(n!)[2]; a:=add(b[k][1]*b[k][2], k=1..nops(b)); end: seq(P(i), i=0..100); # Paolo P. Lava, Nov 21 2017 MATHEMATICA sopfr[n_] := Plus @@ Times @@@ FactorInteger@ n; a[n_] := a[n] = a[n - 1] + sopfr[n]; a[0] = a[1] = 0; Array[a, 59, 0] (* Robert G. Wilson v, May 18 2015 *) PROG (PARI) for(n=1, 100, print1(sum(k=1, n, sum(i=1, omega(k), component(component(factor(k), 1), i)*component(component(factor(k), 2), i))), ", ")) CROSSREFS Sequence in context: A060139 A266899 A112265 * A160663 A024201 A110443 Adjacent sequences:  A025278 A025279 A025280 * A025282 A025283 A025284 KEYWORD nonn AUTHOR STATUS approved

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Last modified June 1 04:57 EDT 2020. Contains 334758 sequences. (Running on oeis4.)