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 A067008 Numbers n such that sum(k=1,n, A008472(k)) divides n!. 1
 2, 5, 7, 10, 13, 16, 19, 20, 31, 34, 37, 40, 41, 44, 46, 48, 51, 53, 55, 56, 62, 64, 65, 67, 68, 69, 73, 74, 76, 79, 81, 82, 83, 84, 85, 86, 87, 89, 95, 96, 97, 99, 100, 101, 106, 107, 108, 109, 111, 112, 115, 119, 121, 122, 123, 124, 133, 134, 135, 136, 137, 138, 143 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 4114 terms from Daniel Starodubtsev) FORMULA a(n) seems to be asymptotic to c*n with c=2.3..... MATHEMATICA tot[n_] := tot[n] = If[n < 2, 0, tot[n - 1] + Plus @@ FactorInteger[n][[;; , 1]]]; ef[n_, p_] := Block[{c=0, m=n}, While[m > 0, m = Floor[m/p]; c += m]; c]; ok[n_] := n > 1 && AllTrue[ FactorInteger@ tot@n, #[[1]] <= n && ef[n, #[[1]]] >= #[[2]] &]; Select[ Range@ 1000, ok] (* Giovanni Resta, Dec 13 2019 *) PROG (PARI) for (j=2, 143, if(!(j!%sum(k=1, j, vecsum(factor(k)[, 1]))), print1(j, ", "))) \\ Hugo Pfoertner, Dec 13 2019 CROSSREFS Cf. A008472. Sequence in context: A255774 A081838 A057347 * A189757 A094065 A073593 Adjacent sequences:  A067005 A067006 A067007 * A067009 A067010 A067011 KEYWORD nonn AUTHOR Benoit Cloitre, Oct 03 2002 STATUS approved

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Last modified February 24 15:59 EST 2020. Contains 332209 sequences. (Running on oeis4.)